As you're likely aware, you can view the date an account was created (month.year) by checking the Achievements page for the account in question. 

But if you want to get more specific and find the exact day an account was created, it is a bit more complicated. There is no direct way to find the day an account was created, but you can try some snooping around to make an approximation.

Let's take a look at the account of an old Ambassador, 12foxy12. From her achievements page, we can see that her account was created in October 2008. Now, let's try to narrow it down.

First, we can try performing a custom search of WeeWorld, using the search term "12foxy12" over the range of October 1st to October 31st, 2008. As you can see, no results were found. Had any messages she sent as a new user still been present on the website, they would've shown up, and we could've used the send date to approximate the day she joined.

Next, we can try using Wayback Machine to find the earliest archives of her homepage. As you can see, the earliest result is from 2010, which is of no use to us.

In conclusion, it is possible to figure out the exact day an account was created, but very difficult. Using the methods described above should be helpful, and will be more successful with newer accounts than older ones.

Good luck!