The Bible also talks about lengthy periods when God was not speaking to Israel. This occurred during the time of the Judges and in the run-up to Samuel, for one, but there are numerous further examples.
In fact the Bible talks about a series of interventions whereby at critical times God showed Himself, but even when you talk about burning bushes and visiting angels, very often these were to very limited numbers of people who believed already, so they were not to make unbelievers believe.
The accounts of them are what are supposed to make unbelievers believe. If you perform a miracle in front of someone, in lab conditions so to speak, then their acceptance of it has nothing to do with belief, it is a proven fact. It is knowledge.
We’re not saved by knowledge, we’re saved by belief. This is intrinsic to the Christian message. If it were not so, then either we would be showing you God or we ourselves would have to abandon Him. But the point is that salvation is through faith and you can only actually have faith through “hearing” (which includes reading, but at any rate a second-hand account).
Those who believe already may receive or may not receive first-hand knowledge of God. They may receive healings and see things which are unlikely to pass as mere coincidences. Their accounts in turn may be believed or not by other people.
That’s how it works.