Yes, you can get the payment gateway with help of your PAN and bank account information, however your monthly limit will be 50,000 and settlement will be kept on hold until you submit the business documents.
You can simply visit https://udyamregistration.gov.in/ to register as an MSME. This can be done using Aadhar card number, with or without PAN card. Please read this article - https://business.paytm.com/blog/a-complete-guide-to-msme-registration-in-india/ and follow the mentioned steps to get your Udyam Registration Certificate online within few days.
Once you have the certificate, you can apply for account upgrade.