We can, and do, observe the effects of the beginning - and we observe those, as noted before, in a variety of ways. Any presuppositions arise because observations suggest such suppositions are plausible. That plausibility is then rigorously tested and rejected, or amended as required.
Might the current, provisional conclusions be wrong? Of course they could.! That's central to the modus operandi of science, but because of the rigour of the investigations, the cross checking, the aggressive questioning of any conclusions, the end result represents the best current explanation for a given phenomenon that is consistent with the evidence. i.e there isn't a better current explanation.
I need to answer your second question a second time. because you seem to missing something. The heart of science is to say "hold on, are we sure? Is this the best explanation?" and then to go out and try to answer that question. So, when you say "But it can’t observe the beginning, correct? It has to rely on presuppositions, which could be wrong." you appear to think you have identified a weakness. You haven't. You have identified a strength - one of the tools of science: always doubt, always question, always test.