What happens when my new Mac has less hard drive space than the old Mac did? Can I recover my time machine back up to an external device?

My new Mac Mini has 500 a GB SSD, while my old iMac had a 3TB drive. There is obviously not enough room to recover everything from my external Time machine back up to this new machine. Is there a utility that can be used to recover data from the old 3TB drive (time machine) to an external drive? I hope I'm being clear, I'm not asking to move the time machine back up from one external drive to another.. I'm looking to recover files, ie extraction of files from time machine to another/ larger external device. Thank you for your thoughts on this.