Will there be a format of play where you are able to play with any of the previous or current cards like in Magic the gathering?

Yes, Infinite. Also depends on the people you play with.

so is the format called infinite?

https://www.fantasyflightgames.com/en/news/2017/11/8/swd-what-lies-ahead/

http://yourdestiny.dk/blog/understanding-rotation-and-format-in-destiny

All sets and cycles are the Infinite format. Those links above should help with your understanding.