Honestly, I would say this phrase once you have a short or full-feature script that you are officially attached to produce AND you are actively putting a team together and approaching investors.
Just searching for a script isn't enough, unless you already have a resume of producing films. Mid-writing isn't the moment either. True producing comes when you are ready to build a team to make a movie and find the money to make it.
You may balk at this but there has to be some sort of benchmark that a producer has to reach in order to be considered a true producer. You could search for or write a script forever. But committing to one when it is ready for the development phase and actively building the team and searching for the financing is the most appropriate time to say you are a producer. It shows you are truly committed to your role as leader of a production. There are exceptions to the rule of course. If you find the money to pay the writer then by all means, you are a producer.
It's true that producers attach themselves to pitches and help create ideas for movies. But for the first time you reveal to the world that you are a producer, I really think you should be at a phase that is further along. Once you are able to get pitches sold then you can say you are a real producer. If you can get a pitch sold without ever making a movie and remain attached as a full producer then by all means, you are a producer. You have surmounted the odds. You have earned the title!
Part of my reason for having a high benchmark for saying you are a producer is because producing is a really tough job and so many people throw the producing title around like it's candy and making a movie is not like eating a box of chocolates. It will kick your ass so hard you will need a box of chocolates at the end of every shooting day. So out of respect for what producers do, I have to remain steadfast in this belief that you need to earn the producing title.
Or maybe it's out of a sadistic tendency to want others to go through the pain I have had to endure before he or she can really say they are doing the same job? Maybe?!
It's sort of like saying you're a full professor before you've even gone to college. That would never happen. So why say you are full producer without having worked your way up on the development and production of other films and then been mentored by a producer into the coveted title?
In the end, this is my opinion. But it's based on over a decade of bearing the weight of multiple productions and wading my way through the ups and downs. I'm pretty passionate about my job and have such huge respect for producers. I hope those just starting out can understand that we were once where you are and we sympathize. It's tough and we know how hard it is to wait to take on the lead role. But, if you love it and can't see yourself doing anything else, it will happen and, if you take it slow, you will be ready.
Be patient. Work hard. Support those around you and they will support you. Love what you do. Be positive. Respect the work of everyone. This is your life. Take care of it.