Would Jesus have been familiar with the Siddur?

I've been reading a lot from Messianic Jewish sources. I'm really interested in the [Siddur](https://en.wikipedia.org/wiki/Siddur) , but I can't find any sources which can tell me if the prayers and rituals in the Siddur were practiced in Jesus' time? Basically, I'm trying to figure out if the prayers in the Siddur are prayers with which Jesus would be familiar.