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OP can still apply to immigrate through a program like Express Entry.

However getting any sort of temporary visa approved (e.g. visitor visa, work permit, study permit) is probably out of the question now.

Yes. As an update, I have been recently rejected my study permit due to the same issues. I'm now preparing for Express Entry route.

Thanks scylla for your guidance !
 
Yes. As an update, I have been recently rejected my study permit due to the same issues. I'm now preparing for Express Entry route.

Thanks scylla for your guidance !

That's the right decision. Good luck. Make sure you declare all of your past refusals in your application. Provided you do that and have enough points to be selected, you shouldn't have an issue.