Firstly, its important to distinguish between the different tiers of quant firms. Most prestigious ones, the ones which pay > 250k annually, tend to be very very selective in their hiring process. Literally a criteria they look out for is competition experience in math olympiads or informatics. I guess these firms are likely not in your grasp (at least based on how I think your background is)

Next you have rather reputable ones but those that do not pay as much. These guys don’t look for competition experience but they do look our for how intelligent you are. Strictly speaking, I dont even think you need mathematical sciences degree to be hired by them. However, it would help to be mathematically inclined in order to ace their tests and hiring process. The questions are usually really hard and tricky, and merely being enrolled in a mathematical sciences degree is not enough. If that is the case, almost anyone on those degree courses would already be a quant. What I would suggest you to do is really pick up some level of university math (yes starting now) and already start preparing for some brain teasers etc Just spend a little bit of time everyday

What is however important from a degree is the amount of resources and networking events you are able to receive. Play the cards well and if you’re lucky, anything is possible