Started with a very low starting pay as I was from a private university. Now I struggle to close the gap between peers of the same age but it's difficult as increment is slow. How to expedite pay?

Gain the experience, and then shine the limelight on the experience to job hop and nego a better pay

You may wish to have a conversation with your supervisor to determine how your pay can be increased which most times would require you to take on additional responsibilities or new scope of work but to be ready for these challenges, do a self-check on your skills inventory to ascertain when you will be able to manage the new tasks because you also don't want to set yourself up for failure. If the conversation with your suprvisor does not yield positve result in terms of you knowing how you can grow in your career which could translate to a better pay increment then you might need to explore greener pastures elsewhere. To do so effectively, it still boils down to what you can potentially offer to the next propsective employers in terms of your value prepositions because if the next employer is convinced you have the perceived contributions to offer to the company, they would most times than not be prepared to match your salary expectation to bring you over.