Question on Time machine migration after setting up new Mac

I have an old Mac I need to get rid of, and a brand new Mac I need to set up sooner than the time it would take to migrate files, or restore from time machine. I was wondering if there would be any problems if for the sake of time constraints, set up my new Mac, and at a later date, transfer all the stuff I want to keep, from the time machine (having backed up the old Mac), to the new Mac. Please anybody let me know if you can. Thanks.