How to validate demand and run the business without building fancy website yet?

Here's what I would do. Find and vet one good specialist. Perhaps for just one of the platforms. Have them at the ready and tell they they'll be paid per job. Validation comes when someone hands over their money for your service. I'd then share and promote the service everywhere I could. I would do it founding members style... meaning, I would promote that I'm launching a new service and looking for a few founding customers to help me shape this into the perfect service for them. In return they'll get a deeply discounted founders rate, which will stick with them for x amount of time. If you get a few buyers, you have validated the service. You connect the buyers with your specialist manually and off you go. Don't need a website for any of that!

1) Test the market with a proof of concept product, as long as it serves your target use case
2) Be transparent with your clients: they can provide feedback on your ideas which you haven't thought of
3) Find an industry specialist who's willing to provide constructive feedback: don't be afraid of criticism

Hi,
With social media platform as something at your fingertip why not use them to your advantage. Go ahead and use all the platforms available to your disposal . Facebook, Instagram, twitter are just a few.
Send it to your friends and colleagues platform as well and ask them to do send it to their friends and colleagues.
You may also do email listing
SMS blast
And of course the good word of mouth.
Be passionate about what you are offering and watch as it grows on you as you get excited about what you are offering.
Hope this helps