Sorry if this sounds silly, but have you all ever faced a scenario where one of the tabs needed to be mandatory (picture below), and the user can't submit the form without addressing that particular tab?
Try using a stepper instead of a form. Tabs are often used as a UI space tradeoff for complex details, and don't imply any actions or sequence.
I might not have the details of your use case, but it seems if it's a form, you want to suggest there's component parts of a total entity.
Using a material stepper is one option, and you can number the steps as an option as well. I'm not sure if your form has lots of optional elements, so in that case you might not need a 'done' checkmark for a section.
This is often the compromise between a developer (hopefully not a designer) wanting some flexibility for the user to provide input but still needing to make sure that a lot of information can be submitted without error.
Otherwise they could either create a wizard/progress workflow and simply not allow the user to continue without completing the previous section or break the input down into smaller sections so it doesn't need to be grouped into a tab.
The 'mandatory' tab, or rather a form of 'input group' validation can be a rather unsightly UI pattern but not impossible to understand for the user. I think it also depends on how the content in the tab is designed but unfortunately it is not as unusual as you think it might be :p
When I faced a similar issue, we created a "General" tab that had everything that was essential to fill out. The other tabs were options they could select if they wanted to. This was for the "Edit Assignment" dialog of a course management system, so the general tab had the name, description, due date, and points. Other tabs were "Scoring" for adding more complicated scoring issues, "Online Submission" for assignments that had online submission and had some options, etc. The point is that everything that is essential to creating an assignment was visible from the "General" tab, but the more complicated options were in other tabs.
If all of the "essentials" do not fit on one tab, I suggest a stepper like other answers.