I’m assuming that Twitter has archived all of Trump’s tweets to comply with the US Presidential Records Act, apart from the White House duty to do the same. All communications of the president, including made electronically, are presidential records and public property.

Even tweets later deleted by Trump are presidential records. A US law requires that all electronic communications to be archived.

The same US law was the reason why Obama had to give up his favorite Blackberry when he became president in 2009.

There are websites that unofficial and independently archive Trump’s tweets, including deleted tweets:
https://factba.se/topic/deleted-tweets
http://www.trumptwitterarchive.com 
https://projects.propublica.org/politwoops/user/realDonaldTrump

The law on presidential records was a response to Richard Nixon’s attempt to destroy Watergate evidence and records that would have led to his impeachment.