Finally found a way to get Sims Legacy to work!
Hopefully this helps someone else! I bought the game on 01/31 and haven't been able to get it to work at all despite trying every fix I could find online. At first it was crashing immediately on launch and after the updates were pushed from EA I was getting the vulkan error message.
Turns out Nvidia pushed a new graphics driver on 01/30 which is what caused the issue for me (and probably a lot of nvidia users).
At first I tried downloading the new graphics card and kept getting an error message form nvidia. So I had to go into add or remove programs and delete my current graphics card, then I had to go onto the nvidia website and download the newest version of nvidia from there.
After I installed that, I updated my graphics driver and the game finally opened and I played through the whole tutorial with no issues! I hope that this helps some of you guys, I was literally so angry and I'm happy to finally have my game working.
Happy simming <3