Unfortunately, with an account as fresh as yours, you really are at the mercy of RNG. If you are really desperate for it then by all means keep running strikes / nightfalls, but know that it is a rare drop. Bear in mind that the game isn’t designed to give you everything all at once, if you had any other catalysts drop whilst running strikes / nightfalls then in all likelihood the number of strikes you’ll need to run has gone up. There is no evidence that using the weapon increases the chance of it dropping, nor is there any that you need to run with somebody else using it. Once you have the catalyst however, you will then need to run in a fireteam using the weapon. Further, running raids is not of any relevance as it only drops from strikes / nightfalls. Edit: typos - make a lot of them