tl;dr You’re a lot closer to being able to do this than you might think, but you should consider a PhD if you want to do research heavy work.
I think at the risk of repeating what has already been said, it has been my personal experience that computer scientists are essential collaborators in some of the biggest undertakings, with often times having very little physics background.
For context, I’ve been doing computational physics research for some years now with relativistic modeling, and there have been almost as many computer scientists as physicists that I’ve run into (regarding large projects) because at the end of the day, a physicist will be better at physics and a computer scientist will be better at computer science, and you need both in large amounts on these projects.
My advisor has been working on a numerical code for gravitational wave modeling, and the group of people working in the project are just two physicists and two computer scientists, because the code is absolutely massive, with so many moving parts, and while my advisor is quite good at coding, at the end of the day a lot of physicists end up being self taught as far as coding goes (or at the very least, with very little formal instruction) and so the perspectives of computer scientists become so valuable in these contexts.
I also have a friend who’s background is entirely in mathematical computing who just got into his PhD with an advisor doing numerical relativity as well, with little to no physics background.
At the end of the day, while all of these experiences are super anecdotal, I think if you’re serious about wanting to change your career to this, you should consider pursuing a PhD, because while a lack of physics background might not disqualify you from a (CS related) position, a lack of a PhD might (big emphasis on might) based on the exact nature of the job you’re seeking. The closer you want to be on the front line of doing cool research, the more likely you’ll need a PhD.