Sure, you can close on the sale of one place the same day you buy another, using the proceeds from the sale earlier. WI is a table funding state, it is usual and customary for sellers to walk out of closing with a check.
You need to coordinate in advance, advise closer 1 of who will be closing closing 2 to make sure they are comfortable accepting a trust account check from closer 1. Also, closer 1 needs to know you will be taking the funds directly to closing 2, and that a "dry closing" is unnacceptable.
Closer 1 will need to be sure your buyer's closer understands that they need to be prepared to fund in accordance with Wisconsin's "Good Funds" law that, basically, requires that collected, good funds be available and on hand at the time the closing is commenced.