I've done that trip several times delivering boats from St Clair for the Chicago to Mackinac race. Its about 600 miles, and takes us about 5 days. We are normally on a tight schedule and do the whole trip Non-stop, except for fuel, then get right under way again.
Depending on the type/size of boat, presumably a power boat, you could do it in 3 days, only running about 10 hours a day. The big limiting factor for a power boat would be bad weather. Running into 5 ft seas for several hours is no fun, and will also slow you down quite a bit. Better to build in a couple extra days for that, and enjoy some of the many small towns with their great harbors along the way.
Lk Huron is known for its very rocky shore. Stay at least 3 miles off shore 30 miles each side of Harbor Beach. You could be running in 50 ft of water that suddenly drops to 25ft. There's boulders down there the size of semi trucks, and quite a few unsuspecting pleasure boats have been destroyed along that shore.
Another thought, we do multi day non stop sailboat trips all the time. But powerboats are a lot different. Most folks find the engine noise & pounding in rough seas uncomfortable for more than 5-6 hours at a time.
Also, the 600 gallons of fuel will cost about $3000. If you're going to burn through that much fuel, I'd rather stretch the trip out to 10 - 14 days, and enjoy your vacation.
Especially with a new boat, keep a close eye on those Temp, Amp & Oil Pressure gauges.