First of all, I would like to stress that in this context "creationist" does not mean "someone who believes there is a God who created the universe" in general. Creationism in this context is a very specific set of dogmas which is based heavily on the more or less (usually more) literal interpretation of the creation story of the Bible. A common characteristic of creationism is that it rejects modern scientific theories on how the universe, the Earth and life was formed to the state we see it today, as they see it as completely contradictory to what the Bible teaches.
(Some vocal creationists go even further, all the way to outright conspiracy theories on how scientists are in a large conspiracy to brainwash people about the non-existence of God by, among other things, destroying and hiding evidence of anything that would contradict established science.)
In most cases these people are so-called "Young Earth creationists", who believe that the entire universe is literally about 6000 years old, but these extreme views on science are not completely exclusive to them, but are sometimes at least partially shared by also more liberal-minded creationists.
There seems to be a very common misconception among creationists (and even more generally among religious people) about what "the theory of evolution" really means and what it encompasses. It seems that to these people the term "evolution" encompasses the majority of what is called natural sciences. They also make all kinds of claims of what evolution claims (or doesn't claim) which just aren't true.
The following are actual claims made by many creationists (not necessary in these exact words, of course).
(Almost direct quote from a video from "The Way of the Master" video series.)
No. There are actually two misconceptions here.
Firstly, the theory of evolution says no such thing. That's because the theory of evolution belongs to a completely different and unrelated field of science.
The so-called "Big Bang theory" belongs to the field of science called astronomy. The theory of evolution belongs to the field of science called biology. You could probably not find any other two branches of science which are more unrelated to each other than astronomy and biology. They have approximately nothing in common. Perhaps the only common thing between the two is that both are classified as natural sciences.
Secondly, and perhaps more surprisingly to many people (even non-creationists), is that even the Big Bang theory says no such thing.
The Big Bang theory does not claim that everything appeared from nothing. In fact, it says nothing about where or how all the energy in the universe came to be. What the Big Bang theory says is that at some point all the energy in the universe (as well as time and space itself) was concentrated in a singularity, from which it expanded. It does not try to claim where that singularity came from.
Scientific conjectures about where the universe came from originally is part of a slightly more informal branch of science called cosmogony. There is currently no widely accepted conjecture (much less a theory) about where everything came from. In fact, and on the contrary, the current stance is more like: "there is no physical model that can explain the earliest moments of the universe's existence (Planck time) because of a lack of a consistent theory of quantum gravity."
In other words, established theories don't go back even all the way to the initial singularity, but just slightly after it started expanding. What happened before that cannot currently be even conjectured.
Often when creationists attack the theory of evolution, they will deal with things like stellar evolution and the formation of elements (heavier than hydrogen and helium).
Again, the theory of evolution says absolutely nothing about those. Just because the term "stellar evolution" happens to also have the word "evolution" in it doesn't make it part of the same field of science, much less part of the same theory.
Stellar evolution and the formation of heavy elements is, once again, part of astronomy (more precisely astrophysics), not biology. They are completely unrelated fields.
No, the theory of evolution says no such thing. The theory of evolution takes no stance on how life came into existence in the beginning.
The field of science which studies how life on Earth could have arisen from inanimate matter is called abiogenesis. It's not part of the theory of evolution, which takes no stance, as already said.
(This is a pet peeve of, among others, Kent Hovind, a very vocal Young Earth creationist.)
Again, the theory of evolution says no such thing. Paleontology and geology are the fields of science you are looking for.
The theory of evolution is the study of how genes in large populations of animals change over time. It doesn't make claims on what happened 65 million years ago. That's what paleontology and geology are for. (Paleontology is somewhat related to, but not the same thing as, nor a subset of, biology.)
A much stranger related misconception (advocated by Kent Hovind and many others) is that if it was suddenly discovered that (for example) dinosaurs did not go extint 65 million years ago, as is currently believed, it would somehow discredit the theory of evolution. I really can't understand where this notion is coming from. Dinosaurs going extint 65 million years ago is not a prediction of the theory of evolution, and as stated, the theory of evolution says absolutely nothing about when some particular taxonomic group might or might not have gone extint.
It's rather ironic and somewhat tragicomic that many vocal creationists seem to think that they know what "evolution" really means, better than evolutionists themselves. It's sadly common that when creationists ask evolutionists for actual proof of the theory of evolution, of evolution being currently observed, and when the evolutionists give them examples, the creationists will invariably claim "that's not evolution". As if the creationists knew better what "evolution" really means.
Of course trying to get out a coherent and consistent definition of what evolution really means is quite a hard task. This also suffers heavily from moving goalposts (in other words, when a creationist gives a definition what would satisfy him, and then an example of exactly that is given, the creationist will then add even more requisites in order to invalidate the example).
You will see many creationists acknowledging that variations can happen to a species over time, but that is not really evolution. You will even see some of them acknowledging that speciation will happen over time (iow. two isolated groups of the same species changing over time so much that they cannot interbreed anylonger, making them thus by definition two different species), yet somehow that isn't really evolution either.
Of course both of those things are precisely evolution in action.
To creationists "evolution" seems to be some kind of mythical concept that can never be achieved (as goalposts will always be moved farther as new evidence and examples are presented to them).
Of course this mythical "evolution" in creationism lore has nothing to do with how science defines the theory of evolution.
It is rather curious how creationists on one hand greatly expand the concept of "evolution" to cover wide fields of natural sciences (which have absolutely nothing to do with it), while at the same time reducing its coverage from phenomena which do clearly and unambiguously fall under the concepts of evolution.