Do we simply base them on our nearest competitor (we don't have any that are direct competitors, but lots that are vaguely competing) or do we simply base it on our user feedback surveys we ran before coding? (eg, 80% of n users said they wanted a service that ...)
Other than that your only option is to use a crystal ball, I don't think it is any use at all to try to do these predictions but I understand it is part of the game. You'll only have the data you need now when you're operating for a long enough time that you have seen several full account life cycles so that you can refine your predictions.
Your nearest competitor isn't going to be much help to you because for one they are established, and secondly they may do a much better / much worse job at retaining their users.
Every web site will start off great at launch time because there is nobody leaving (yet). Once you factor in churn you're in a much better position to figure out how big something will be over time but for that you need your actual data.
Usually, they shake their heads and say "They'll make money no matter what."
At least, that's been my experience.
I financial model my numbers based on all the possible inbound factors and growth rates. Just build it in excel with the input factors and change them based on logical assumptions.
Run google ads for a product that isn't there yet - if users click your specific advert you know they're vaguely interested in it.
1) A new AdWords account starts with no history. To get preferable placement you'll have to be significantly outbidding the people who already have history. (i.e. I pay Google four cents a click for front page placement for, I don't know, [how to make a bingo card]. If you started a new AdWords account today Google would charge you a quarter.
2) There are automated quality checks which score sites these days and can raise your minimum bid to stupidly high levels, which is essentially Google's way of declining your business. If you put up a page for a product which doesn't exist, you are highly likely to have these checks fire on you, since they're specifically designed to bounce squeeze pages.
3) Getting a click on an AdWords ad doesn't prove the customer had interest, it proves that you wrote the ad well. Conversely, not getting the click doesn't prove there was no interest, it merely proves the ad was not interesting. Do you have someone in your organization skilled at the art of writing 3 line advertising copy? If not, what are you burning money for?