How can I convince my company that we need to invest time back into the products we offer?

This is a pretty classic engineering problem and is ultimately an exercise in communication. Because of that, I highly recommend going through my series on Effective Communication here.

Here's my main thoughts:

• Understand the GTM team's incentives - Good engineers value building good software. The problem is that almost nobody else will value and appreciate the same thing, so it doesn't make sense to anchor the discussion along these lines. The GTM team's goals are probably to make the clients feel special with a clean product and to do it fast.
• Connect your problem to GTM's incentives - Off the top of my head, I see bugs and velocity as the main things to connect to. Having custom solutions for everything stresses out the engineering team, which will lead to worse product quality. If you can draw those lines in a formal proposal, that would be very powerful. Show how building common infra is a "1 step background for 2 steps forward" course of action. The more receipts you have the better (e.g. "With this common infra that will take us 1 month to build, we can ship 5 solutions with 2 weeks each as opposed to each solution taking 4 weeks without the infra).

Lastly, this Q&A is a pretty different issue, but the problem is largely the same in terms of archetype so I recommend reading it as well (misalignment between engineering and non-engineering).

Data wins all arguments, especially for an audience like yours, where it sounds like they really value throughput. You probably want to make the argument that some eng investment will either:

1. Reduce the time to build custom features or
2. Reduce the need to build custom features at all

Can you construct a very simple and clear argument on how some upfront engineering will lead to a nice ROI? Not just a 2x improvement, but something like 5x. You can make the argument both in terms of time savings, but also engineering happiness (some companies have an entire team called "developer experience").

Finally, could you do this without needing permission at all? Just go off and build something small which leads to some time savings, and let the other engineers know about it. If you can make quick progress, it's better to ask for forgiveness, not permission.