That is how "Big Bang" actually started - by observing the fact that a space is expanding (about 100+ years ago). Then Einstein solved his GR equation for universe as a whole and found NO stationary solutions (= a rock can not "hover" in the air if there is gravity. It should move.
And indeed it expands as seen in any good scope with a spectrometer).
If it expands, then it was smaller in the past, right? And perhaps very small in the very distant past. Do you deny the statement that presently expanding things were smaller in the past? (Basicly, this is the essence of Big Bang).
In 1961 cosmic microwave background radiation (CMBR) was discovered and greatly substantiated idea of space expansion by showing that distant (=early) universe was much hotter than the present day one. Indeed, working against gravity energy of expanding e/m field turns into gravitational potential energy, so temperature of field (=photon energy) drops. Joe, do you say that you do not believe that CMBR is there?
Later numerous modelling of expansion predicted certain H/D/He/Li/Be ratio left after the temperature of expanding universe dropped below energies of nucleosynthesis. And indeed, these abundances agree with observation (taking into account futher history of universe). You don't believe in this too, huh?
Important remark. Often I hear in this forum that "Alex, this is your PERSONAL opinion (theory, guess, hypothesis, bullshit, Language Removed, scientific garbage...)" (different people use different words to label what I say)". Let me claryfy that it is NOT MY. Joe, everything I printed on this forum, (with very little exception) is NOT MY THEORY contrary to your claim and firm believe. THESE ARE FACTS FROM TEXTBOOKS AND FROM SCIENTIFIC OBSERVATIONS PUBLISHED IN SCIENTIFIC JOURNALS (plus mathematical explanation of these facts, mostly also from the same textbooks).
Joe, if you do not trust facts consistently observed by scientists (like red shift, CMBR, etc), then you probably one of those people who believe only in what THEY PERSONALLY see, hear, smell and touch. Thus, then you simply UNAWARE that there may exist things smaller than your eye can resolve and father away from you than your hands or nose or eye can reach.
Unfortunately, in this forum we do not have time and space to explain you such basics.
Fortunately, there is very good place where you can get this information - called elementary/ junior high school (look up in yellow pages - there should be some near you). Teachers there are professional experts in educating humans with zero or very limited knowledge (like yourself). Especially I recommend attending math and science classes. There they explain you basic facts, basic natural laws, basics of how and why things work.
And it won't cost you a penny - these are tuition-free institutions, and all textbooks are free too.