You can enter the Quetico from the US side. You will need both a remote entry permit which allows you to enter the quetico without passing though a formal customs check point, and you will need a permit for camping in the Quetico. You can get more information here:
Quetico Parks You need to do this soon too. The permits fill up fast for the Quetico. It is possible to get away without a reserved BWCA permit (just a day use permit) if you only paddle in the BWCA for a day and do not spend a night at a campsite.