I'd like to see the first tweet of a Twitter user. Is this possible without clicking "more" a hundred times?
There's a #FirstTweet for everything.
Find anyone's first Tweet. Just enter the @username below to get started — where it all started.
Please note that if the user has a protected account, this tool doesn’t work.
http://myfirsttweet.com should do exactly what you are looking for.
First Sixteen Tweets (or as far back as it can go)
Tested it myself with the More button Here is how
Copy the link of the More Button and you are going to change the PAGE_NO to larger values until there are no more tweets (blank) then decrease the value/increase the value. Much Faster than clicking more.
The only other option is to follow the Library of Congress since they have have acquired all of the tweets since 2006 and see if/when they release it.
You can use Twitter's advanced search operators to search for tweets from a user, within a date range you suspect their first tweet may be (e.g. soon after sign-up). You then might have to scroll down a bit, depending on how often they tweeted and the date range you chose.