The approach that will continue to work for start-ups (both from Europe, eg Sweden is good at this, and the US), is to build out your service in the US first, monetize it there, and then push into the EU once you can afford compliance. This is already the ideal approach, anything the EU does to make regulation worse will merely increase the advantage of using the US as the springboard market. There's absolutely nothing stopping EU start-ups from first focusing on capturing the US market and then turning their focus back to the EU.
There's another approach that is less legally certain. Build up users in both the US and EU, and only monetize the US users while entirely ignoring all EU law. You allow EU citizens to sign up, and do not place any infrastructure in the EU or do any business there initially. Jurisdiction will be in the US. The monetized US users, which will remain lucrative, subsidize building out into the EU member state markets without any revenue generation. You capture the EU userbase in this approach, then later comply with EU law and monetize that userbase after you're compliant. Would work best for ad platform businesses like Google, Facebook, YouTube, Instagram, etc.
If I'm operating a service in eg Brazil, I have zero obligation to comply with EU law (depending on treaties of course), nor do I have any responsibility to block EU citizens from signing up for my service. Let the EU users come in, comply with EU law later when you have to in order to monetize the market. Retro fines are one potential concern at scale, however that ends up being the equivalent of a speeding ticket and you own the market.
One of the mistakes that keeps being made by EU tech promoters, is thinking that they should be concerned with competing with the existing US mega platforms (such that the EU needs to build a search engine to rival Google, photo platform to rival Instagram, mobile platforms to rival iOS or Android, etc). That battle was over a decade ago or more in some cases. The focus has to be on the next inflection point opening that allows for a creation of the next mega platforms. With platforms and the Internet, if you don't capture the US market first, the winner in that market will almost always smash you (or buy you) unless you bar access to your market as in the case of China. That's due to the enormous monetary value of capturing the US market (and you pretty much get Canada with it automatically, a $1.7 trillion economy), it acts as a perpetual well of resources to over-spend on then divide and conquering other markets like the EU.