I don't know of any private shops around here likely to rent space or tool usage. University or community college wood shops will often have membership/rental programs available though (for the few that haven't already closed their wood shops.
) A good portion of the most needed tools are specialty tools anyway that you will be best just investing in if you want to get in to building.
There is a Michigan Guild of Luthiers group that meets on occasion around here. The last meeting was here in Ann Arbor some weeks back, but I'm not sure when or where the next will be scheduled.
In any case, start your investing in books and research before tools.