It depends on whether a baby is non-negotiable for you or not. If it is, then I think waiting 3 years carries the risk that you may not be able to conceive, or may need fertility treatment. if that is not something you can countenance, then I think you need to be clear about that with your partner. If it’s a dealbreaker for you, he may be willing to try now. If he isn’t, then you have a decision to make- end the relationship and move on, or accept the risk of ttc later with statistically reduced chances of conceiving (not zero, but significantly reduced).
Equally, I think having a baby whilst trying to study at university level is not an easy thing to do- if this is something he really wants to do and he will only get this shot at it, I can understand his reluctance to have a child right now. You would both need to be totally onboard about starting a family now if he goes to university soon. He might be worried that it puts his ambitions/dreams in jeopardy. His dreams are no less important than OP’s desire/dream to have a baby- neither is wrong, it just might mean that you aren’t compatible.
I would also say that I can understand the worry about having a child you aren’t sure you can support financially. You might not need a mansion and 5 years of income in savings, but you do realistically need to be able to provide essentials. If he is not working/on student loan/grant, then can you support 3 of you on your income and student finance +/- any benefits you may or may not be entitled to? What about when you are on maternity leave (some people have better maternity pay than others). Have you sat down together and worked out if you can afford a child if your partner does go to university.
I am not sure either approach is “wrong”, perhaps case of different priorities/right person but wrong time.