If the problem I found requires a fair amount of time to solve for person 1, do you have any advice to avoid making something that only caters to that person and that’s not extensible to person #2?
It might also be worth mentioning that product ownership isn't intrinsically better than providing a service if you have your business model honed really well. We tend to promote that bigger is always better and that scale is the only way to make money... neither are inherently true.
... but the above comment I was putting forward is based on the team from Basecamp and my business mentors.
Regarding your question: The process takes balance and focus. Arguably, a harder part is customer selection to find the right client to help you with both your short term and long term goals.
TLDR; Custom > Service > Customized Product > product
Longer version with steps:
1) find a problem
2) find someone that needs that problem solved, solve it for them
3) find someone else that has a similar problem, use some of the stuff from problem solve #1 to make this build faster, but build new stuff that the person from problem #1 might want to buy
4) Sell person #1 the stuff from build #2
5) now you have some things that you can try to sell to other people, it will probably require some customization, but you'll start to get the core of your future product in each build
6) after few more customers you basically have your product, you just need to polish it and then take everything you've learned to find more people that resemble the people you just sold to to go find more people.
7) you no longer need any advice from anyone, you are busy selling your product