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Offer PFD on the open collections with a balance, you can sometimes offer less than you owe to start, and go up from there. Dispute anything that is inaccurate. You can also GW anyone that is reporting a late payment. You may have to try all of these methods repeatedly.
Open a secured card as soon as you can. You need a positive TL reporting. Can you get added as an authorized user on someones account? That also helps. Once you have 6 months reporting, check your scores. Once you get a boost, you can try apping for an unsecured account. Google who gave me credit and see what scores you need for certain creditors and you can play with it to see what works best for you.
Good luck and welcome!
You would only dispute something that was not accurate. That would not be my first course of action. PFDs for what's not paid and GWs for those lates would be the first steps.