Here is an approach for estimation that works pretty well (from the point of view of a manager).
1. Ask the dev team to provide an optimistic estimate, and to then multiply by 2 to make it "realistic".
2. On top of that, add another x2 (which can be recalibrated as you learn how accurate this tech team is over time with estimates). Don't tell the developers about this, but make sure your higher-ups understand that this is what they need to be prepared for in terms of budgeting and time limits.
The reason you don't ask the developers to multiply by 4 directly, is to keep them motivated to aim for the x2, and avoid slacking or over engineering while feeling overly comfortable early on.
But by having the extra x2 in reserve, your back is covered, and you can afford to be cheritable with the dev team as they (as usually happens) go a bit over the x2 estimate.
This buys some early goodwill that can later be traded back in if you need them to up their game later on.
The alternative to the above is to exclusively find managers (at all levels) that can combine manager skills with high level engineering skills. Such managers often have the ability to expose unneccery delays directly, which includes the ability to tell apart delays caused by devs slacking from incompetence, scope creep or unexpected but valid causes.
Such people are really hard to find, though, for most companies. But companies that manage to build such high level top to bottom tech lead cultures may certainly be able to go from the 4x back down to 2x or even 1x compared to companies with non-technical managers.