You can actually view the times of some of your promotions that were tracked by the site by appending ";displaytype=xml" to the URL to your own "home node" and searching for "levelchange". For example, ?node=u65;displaytype=xml will show (only to u65) information that includes timestamps of level changes (that happened during the time window when that feature of the site was working).
set term pngcairo size 1024, 800
set xdata time
set timefmt "%Y-%m-%d"
set format x '%Y/%m'
plot 'pm-xp.txt' using 2:4 with lines title 'XP',\
'' using 2:($1*1000) with lines title 'Level',\
'wayback.txt' using 1:2 with lines title 'Wayback Machine'
<joke amount = "half">
Between, Super Search, Levels of Monks, and by following the dates, it can be approximated. (Voting/Experience System explains how points are distributed.) Of course, you'll need to vote on each node, which might take a while and would have to be incorporated into the approximation. XML might make it a bit easier.
I'm kind of interested in this. Specifically, to know what level a monk was at the time of a specific post. So many forums tell you what the user is now, which is redundant, misleading, and not applicable to the post being looked at...unless it's to say, "hey, look at where a post like this might lead." And, it has an extra cost on the system to keep it dynamic. So silly. :)
I don't believe there is a way to know; it might be possible to make good guesses. I'd be interested in chacham fleshing out his ideas.
Recording my own progress is the reason I came up with this. Unfortunately, it can record only the current state, and won't help with history. The wayback machine should help with that, but I'm not familiar with it myself.