Adverbial first is like many other common terms (just, only, etc.) in that we can often be a bit loose as regards exact positioning relative to the specific word (noun or verb) it applies to. Who's gonna argue over whether I only wanted the short answer and I wanted only the short answer mean the same or not? You're gonna get the slightly longer answer anyway.
In OP's exact context it would be equally pointless to postulate different possible meanings, but consider...
1: I must first receive the product before I pay the bill.
2: He received first the bill then the product.
Obviously there are many other positions for first in both of the above - only some of which will affect the meaning (not necessarily unambiguously). Thus, He received first the bill then the product and He received the bill first then the product are valid and equivalent alternatives to #2 above. But note that I must receive first the product before I pay the bill is not an idiomatically valid construction.
Then there are even more exotic ways to play with the position of first...
3: The volunteer went first
4: First the volunteer went
5: The first volunteer went
6: The volunteer wants to be paid to go first
7: First, the volunteer wants to be paid to go
8: The first volunteer wants to be paid to go
9: The volunteer wants to be paid first to go1
Cutting to the chase, by default the word first modifies the word immediately following. So in OP's exact context we could imagine that to first receive suggests that the act of receiving [something] is uppermost in the writer's mind (then maybe he'll think about doing something else), but to receive first a feedback suggests that he's thinking of the things to be received (after he gets the first one, he'll be ready to receive other things).
In practice that's an almost meaningless distinction for the context, as I suggested above. But that's just how it works in English. Not all differences make a difference.
EDIT: Further to comments below, I should acknowledge that with OP's specific pair of possible positions for adverbial first, one of them (to first receive) could be described as a "split infinitive". Mostly today the only times you'll encounter that term is when someone's poking fun at misguided Victorian grammarians who said this was "bad style".
But there is some merit in the advice from Strunk & White that you should avoid splitting infinitives unless you want to stress the adverb. Although having said that, I would add that it's simply impossible to conjecture different meanings for Star Trek's to boldly go [where no man has gone before] and the pedant's (hopelessly non-idiomatic, but mistakenly thought to be syntactically better) alternative to go boldly (which is always the example used to ridicule the "rule").
On the other hand, there is a perfectly credible distinction of nuance with OP's specific example, as outlined above. Since the adverb more strongly associates with the immediately following word, the speaker's choice of position could emphasise whether he's more concerned about early receipt (of whatever), or about the fact that he specifically wants "feedback" first. Sure, it's "splitting hairs", but that distinction does potentially exist.
1 In case this one's a bit tricky for learners to parse, I should point out that #9 is actually ambiguous. Either the volunteer simply expects payment before he will be willing to go, or he specifically asks to be paid before anyone else is paid (if not, he doesn't want to go).