Are miracles evidence of the existence of God?

[Belacqua]

First, one would have to know that whatever happened was actually impossible to have been due to natural laws or causes.  It seems there is enough we don't know about the natural world that that is unlikely to ever be known.

As far as I can tell, in biblical times miracles were not described as supernatural. 

For on thing, our modern distinction between natural and supernatural didn't exist yet. People thought that there were demons, angels, etc., existing naturally in the world. They were just part of the world. And they could do things that humans can't, in the same way that humans can do things that snails can't. 

The original Greek words in the Bible which are translated as "miracle" in English are semeion, meaning "sign," teras, meaning "wonder," and dynamis, meaning "power." So a miracle is a sign from God, a wondrous event, or a show of power. None of these is necessarily supernatural. The Latin Vulgate for these three terms is signum, prodigium, and virtus, respectively. 

The English word "miracle" is derived from Latin miraculum, meaning an object of wonder. Mirari means to be astonished, and mirus means amazing.

So it appears that originally, miracles were thought to be amazing wonderful things, signs from God or demonstrations of his power, but not necessarily supernatural. That's a modern addition. 

Some miracles in the Bible might appear supernatural to us now, like the parting of the Red Sea. Others not so much: when the birds brought bread to Elijah in the wilderness, there was nothing supernatural about that. Birds can carry stuff, and you can even train them to carry to certain places. 

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Also I think we can take different kinds of things as evidence.

An event is not evidence just in and of itself. It becomes evidence when someone takes it as support for a proposition or theory. In practice we use all kinds of things as evidence.

So in science it is better not to use widespread belief or hearsay as evidence. But in life we do it all the time. If everybody in my neighborhood gossips that Dentist A is good and Dentist B is bad, I'm going to take this widespread belief as evidence and choose my dentist accordingly. It's not proof, but it's evidence. 

Likewise for people who already interpret the world as being full of various wonders, an inexplicable or amazing event can add credence to the theories they have about the world. For them, it becomes evidence. 

For atheists, who don't hold to the theory that God acts in the world, we don't interpret inexplicable events as evidence for this.