Automated date/deadline/timeline considering % of Project Phases

Hi everyone!

My company is considering acquiring the Enterprise (we are over 250 employees at the moment in a scale-up), and I am trying to show all the possibilities that would give us, being the best tool for our internal project management. Some things have been required and I would like to know if is possible to get it automated by Monday.

We need to manage projects that have 4 different phases and that depending on when we receive it, each phase deadline would need to get squeezed to fit the general project deadline. Ideally, we would receive a project with 6 weeks to go through the phases: 01 Starting phase, 02 Project Concept & Design, 03 Specification and 04 Submission. Knowing that 01 takes 20% of the time (5 days); 02 takes 55% (15 days); 03 takes 20% (5 days) and 04 takes 5% (1.5 days).

What we would like to do is: setting a timeline for the entire project (from starting to submission) and having an automation to set the internal phases deadline/date.

Is this doable? If yes, how? If no, what would be the suggestion to get the closest to that?

Thank you all!