I’ve found that going by significant digits helps.
“If I represented the date that Einstein came to the US with only one significant digit of precision, what would it be? Definitely 2000. What about two? Definitely 1900. What about three? Probably 1900 again; I’m willing to take that bet. But four digits of precision? I’m not sure at all. I’ll leave it as 1900.”
The answer came out way off, but hopefully it prevented any anchoring, and it also accurately represents my knowledge of Einstein (namely, I know which properties of physics he discovered, and I know that he wrote his most important papers in the earlier half of the 190Xs, which must have also been when he came to the US). In hindsight, I might have should have taken historical context into account (why would Einstein leave for the US in the first place? if I had considered this, my guess would probably have ended up as 1910 or 1920), but that’s hindsight bias or a lesson to be learned.
An improvement to this method might be that I explicitly consider the range of numbers that would make it come out as a significant digit (if the three-significant-digit number is 1900, then he came between 1895 and 1904; does that sound more plausible than him coming sometime between 1905 and 1914?). But this might just make the anchoring effect worse, or introduce some other bias.