Can i claim construction costs of new vacation rental cabin built in 2024 and renting in 2025?

Construction costs would add to the cabin's tax basis (excluding land costs). Since construction was not completed until 2025, it would seem there is nothing to report for 2024 except any taxes and/or mortgage interest that would go on schedule A and be subject to the limitations for 2024. 

for 2025, there is code section 280A that determines the reporting of the rental activity. you may want to discuss this with a tax pro. Depending on rental vs personal-use-days - pud (days rented below fair rental value are "pud"). The deduction of expenses against rental income can be significantly limited. Even if not limited this would seem to be a passive activity unless significant services are rendered to the renters thus limiting losses that could be deducted against your other income.