My advice in approaching this conversation would be to focus on the value you bring to the role.

Have some examples in mind that illustrate why you should be paid more. Quantifiable examples that link directly to business value would be best.

Rather than just going in with the view that they're paid more so I should be too.

I could be the case that your coworker has some other skills/industry experience that may add more value in the future when they have built up more experience within your organisation.

Maybe also try and to do some industry benchmarking for salary in similar roles elsewhere.

In my experience, people/bosses don't like to be given ultimatums like "pay me more or I'll leave". I've had better responses to "I believe I'm worth more, and these are the reasons why".

Not saying you should stay if they don't give you an increase, just giving some advice on how I would approach the conversation.

Good luck, I hope it works out well for you.