When Trump becomes President, Republicans will control all branches of government and both houses of Congress. The only thing a unified Republican Party couldn't do, is pass things which require a super-majority, constitutional amendments, or similar legal action that requires unusual kinds of cooperation.

Will they cut spending immediately, such that the debt will hold constant or decrease?

This question resolves "Yes" if the Debt to the Penny data stream,

https://fiscaldata.treasury.gov/datasets/debt-to-the-penny/debt-to-the-penny

reports that the total public debt outstanding on April 21st of 2025, minus the same measurement on January 21st 2025, is equal to or lower than $1 million. (I.e. "Yes" if the debt does not grow by more than $1 million in the first three months of the Trump administration.)