You can still claim your business expenses on SCH C. Just be aware that if you don't have the business income to deduct them from, then those expenses just get carried forward to next year. Then you can deduct them from the business income next year, provided you have the business income to actually deduct them from.
Also, if you don't "claim" the expenses on your 2020 tax return, then you can't carry them forward to the 2021 return next year. So claim them.
