I had a NEOs website made, and it is currently hosted on A2 but I would like to move it to GoDaddy. I called GoDaddy support and was advised to purchase a GoDaddy VPS. Unfortunately, the developer I’m working with is saying that they tried to host on the GoDaddy VPS, but it is not reflecting on the server. Any advice/help?
Yes, you can do that with their packages, that include SSH shell access.
Be aware, though, that GoDaddy can be one of the worst performance wise, especially at times, when they throttle the web server hosting your site due to their traffic, usage and performance share politics.
I suppose, they recommend the VPS because of that.
If you have ssh AND a working accessible php-cli binary at hand youre fine.
At first i’d see if you can install composer and get it working 
(Sometimes hosters offer a trial - that might help with deciding ^^)