Is it possible to integrate a booking form that doesn't allow the user to select a previously selected date or time?

For example if some other user selected the date for today, starting from 3PM, the user that is trying to book something now will not have the ability to select 3PM for today.

That is possible here in JotForm. Please check our Appointment Slots widget: https://widgets.jotform.com/widget/appointment_slots

Please check these demo forms: 
http://form.jotformpro.com/form/43352010062942?
https://form.jotform.com/71090803677964

If you want to clone the demo forms, please follow this guide: https://www.jotform.com/help/42-How-to-Clone-an-Existing-Form-from-a-URL

Hope that helps. Please do get back to us if you have questions.

thanks for the guide. the same question here!

You're welcome, Noah.

Don't hesitate to open a new thread if you have questions or issue. We'll be glad to assist you.