Just finished master's degree - have I missed the boat?

Hello, this is my first post here so please forgive my naivety if it shows.

I have just finished an integrated master's degree in Mathematics and Comp. sci. at the University of Bristol. If all has gone as I expect, then I should have a first class degree.

Having done this degree for 4 years now, while I find the content very interesting and I am very good at it too, I am very sure that I do not want to persue a typical career for someone in my position. These careers usually involve being a statistician, software developer, academic etc.

I have only just begun considering finance as an option. This mostly was brought about by joining the finance society at my university and taking a 6 month course where I learned about equities and fundamental analysis. I know that this was just the tip of the iceberg when it comes to finance. I did make some applications in the last recruitment cycle. However, since I was not well prepared then, nothing came to fruition.

Having not considered this path properly until now and therefore having not done spring weeks or internships in finance so far, I have two main questions:

1/ Am I too late to start trying to get into finance?

2/ If I am not too late, what should I do from here and what do I need to know?

Any help or advice would be greatly appreciated!