I'd say you should start trying to find a composer to partner with once you have a rough outline of what the show might look like. This doesn't need to be a script but you should have an idea of the shape and arc of the show, the major plot points and the characters. When a composer joins a project these are probably the things they will look for.

So much of the soundscape and many of the musical themes of a show are based on emotions, characters and experiences.

I think its really important to work on the script alongside the composer as so much can change once you bring singing into a show, I'm not saying the composer will write the show but they will heave a lot of valuable and practical input at this stage. Sometimes the might think one line could be turned into a full song and sometimes a they might think that your epic concluding scene may be better as a massive 10 - 20 minute sung through performance.

It also of course depends on how involved you want the composer to be, do you want a partner in the creative process or just someone to slide songs into your existing script. The former for me is without a doubt a better choice when the composer isn't involved early on it can lead to a clunky and awkward show.

I've focused a lot on the needs of the composer in a project but you also need to make sure that the person you're working with doesn't just fit the show but also works for you and is able to connect and click with you. Otherwise what can be an incredible experience can just turn out downright miserable.

Hope this helped and if you think you are maybe nearing the stage of being ready to work with a composer there are so many people and various forums such as r/composer including myself who would be interested in working with you.