It seems like it’d get increasingly impractical as the years go on to hundreds of thousands and millions of years to write them out that way, but then…I guess technically one may already do this with the preceding years, so future’s fair game for it?
Astronomers already use Julian Dates for various reasons. Right now it’s 2460261.2834606, it’ll be later by the time you read this. Julian dates/times are fractional days starting from January 1st, 4713 = 0. Just keep counting up from there.