Trump made the claim via tweet on the fourth and last day of the DNC in which Joe Biden formally accepted the Democratic Party’s nomination.

The claim was false, as each day of the DNC opened with the full Pledge of Allegiance.

Day 1:

Day 2:

Day 3:

Day 4:

“Under God” was omitted from two smaller individual caucus events, the LGBTQ caucus meeting and the Muslim Delegates Assembly. Each day of the DNC consistsed of some half dozen different individual caucuses.

The phrase “under God” was added to the Pledge of Allegiance in 1954 amid the Cold War.

Associated Press – AP FACT CHECK: Trump’s distortion on Dems and the pledge
Snopes – Did Democrats Omit ‘Under God’ from the Pledge of Allegiance?
Wikipedia – Pledge of Allegiance, Addition of “under God”