Getting into data science from adjacent field?

Hi all. I work in simulation consulting at big 4 right now. I came from working in computational fluid dynamics after doing a masters in mechanical engineering.

I've realised it's not for me. I don't get to be hands on with code enough. I hate consulting. I prefer being quantitative and working with code. / being creative.

I thought data science may be a way to go. I've got python and some software engineering. Strong maths from engineering. Very basic sql. Small amount of ML from doing udemy courses and a small bit of on the job work. Basic c++. But I don't have the stats and probability.

How possible is it to do this? Do I need to go and do a masters to do this? Or could I shift from here?