If it is of accounts of the past, then you must look to the past. Archaeology has proven time and time again these things have happened.
No, it proves the bare minimum of superficial detail of past events, certainly nothing supernatural is backed up - and this is then extrapolated to justify the entire set of claims being made.
A bit like how the existence of New York "proves" Spiderman to exist.
Interestingly, there are some claimed events in the Bible where there isn't even the bare minimum of superficial evidence to back it up. There is an utter dearth of archaeological evidence for the exodus, for example.
If it is of accounts of the future, then you must look at what it has fulfilled that we can view. Example is the 1947 of Israel coming back together, a modern miracle for all eyes I must say!
Not really. It was entirely engineered by politicking, and Christian apocalyptic prophesying only gets dates right by spewing claims left right and centre, and claiming accuracy when they happen to get something right.
The Israel of 1947 is also nothing like the Israel of the past, both in territory, demographics and government, so it's debatable whether it's the same thing at all.
If it claims to be without error, then why not look at the law it gives within the bible? You must admit for a people coming from such a land like Egypt, the people there using feces to treat wounds?! to having such cleansing laws that rival todays time. We didn't even know germs existed till the 1800s, and is why we had many babies die because of them washing their hands not under running water.
This does not justify the claim that the entire Bible is without error. Again, the validity of each claim needs independent verification. You can't just sneak a bunch of other claims in because one of the happened to be correct.
They don't rival today's time for the exact reason you point out - we know what causes infection, and WHY washing is important. Mosaic law does not explain these things, it merely states that the Israelites must obey and gives dire threats if they don't. For all we know it is entirely coincidental, and likely was.
I want to say there is evidence if you so choose to accept it. But it is up to the individual to look. As a believer I can only guide, I can't convince your own heart unless you yourself allow such a thing to happen.
You can do better than the above, surely.