Path-finding can be really easy and rewarding to do yourself rather than asking a game engine to do it.

Path-finding works over graphs, so you have a "node" which in your case would be all the squares in the map, and "edges" which are all links between the node and all the neighbouring nodes!

Then you find the version of A* search algorithm package your language has and just pass it the nodes and edges, and it'll return the path of nodes.