Trump will make the government and its cost a lot larger. He is talking about deporting millions. That requires investigations, policing, housing, and transporting them. It will require diplomacy. Some countries will not accept Trump's' decisions about who belongs to them. He is starting new departments. You do not analyze very well.
No, it requires stopping all federal money to "sanctuary" government, requiring a "Real" ID to open a bank account, enter a contract, make a wire transfer, etc., requiring all state and local law enforcement to cooperate in enforcing immigration law, no public assistance whatsoever, and basically making life impossible to live for illegals in the US.
They will self-deport for the most part leaving manageable numbers to deal with by arrest and forced deportation.
As for decreasing the cost of government:
I would tell Trump--if there were a reasonable chance I could--to do the following.
On day 1 in office send out an executive order that every agency and branch of the executive branch within 30 calendar days provide an accurate number by page count and word count of all regulations and rules they have in the federal register.
Once you have that
in writing you then make an executive order that each agency, department, branch, etc., remove by page and word count 5% of the total that was reported above. They have until Oct 1, 2025 to do it, and failure to do so will result in a reduction in budget equal to the percentage of the target 5% not done with their budget in such a case being equal to the baseline budget in 2024. That is, the agency isn't getting any new money and their budget will be smaller if they don't hit that 5%.
Add, that this reduction does not preclude any agency from enforcing all regulations and rules, or making new ones, so long as on Oct 1 they have by word and page count 95% of what they had on Jan 8th.
Wash, rinse, repeat, four times. This results in an approximate 18% reduction in the volume of rules and regulations the executive branch agencies have in the federal register over four years. That will reduce the cost of government whether you like it or not.