So If I understand you correctly
you need to trigger the process when a user click on the button which is in webpage
For that you can build a unattended bot with the Bapi activities
Later you need to build the webpage button like onclick using Javascript where you need to use Orchestrator API to trigger the process
Also you can take a look on UiPath Apps also, you can build a form and you can configure onbuttonclick and choose the process
Hope this will help you
Thanks