After the 2020 US election, suppose that the Democrats end up controlling both houses of congress and the white house, and that their first action is to give statehood to DC and/or Puerto Rico. When would the new senators and congressional representatives be seated?
Let's take the example of Hawaii, which was admitted to the Union on August 21, 1959.
The elections for Hawaii's Representative and Senators were held approximately one month prior to this, on July 28. This allowed Representative Inouye, Senator Fong and Senator Long to take their seats on the day of Hawaii's admission to the Union.
It is probably fair to assume that, if DC and/or PR were admitted to the Union, they would hold their elections far enough ahead that their Representative(s) and Senators would take their seats on the day of their admission.
For the House, they would hold an election when the next Election Day comes. The District of Columbia would elect a Democratic House member, and we think Puerto Rico would, but we do not know enough about it and it elected Republicans in the past despite Hispanics voting overwhelmingly Democratic. Puerto Rico would have about 5 representatives (7 electoral votes) and DC will stay the same.
After the next census, the representatives are reallocated and representatives are changed from 443 (?) to 435. I'm not sure about Senate but I think that it would be staggered like normal and they will be filled.