Parametric estimates are usually the best compromise between speed and accuracy. We were able to define a model with +/- 50% contingency that a Principal BSA or an experienced Sr. Product Mgr can use to give a rough estimate in 5 minutes for front-end developments by identifying teams impacted, type of development and 2 or 3 other parameters. Good enough for quick "continue to deep dive or not worth the effort" decisions.
It's not unusual for non-engineering folk to inquire about engineering estimates and the amount of time they take. What methodology does your engineering team use to facilitate estimating when there is significant time pressure?
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We typically do "t-shirt" sizing for "epics". xS,S, M, L, xL. These represent a range of number of sprints (2-week sprints).
If we are estimating large initiatives we tend to use "squad quarters".