If you start a business and buy all equipment in 2019, but don’t legally start your business until 2020 can you still use those Purchases as write offs in 2020 for taxes?
No. Equipment and other assets can't be depreciated or written off under Sec. 179 until the date they are placed in service. If they are purchased in 2019 but not placed in service until 2020 they will be reported on the 2020 tax return filed in 2021.
For the stuff that doesn't depreciate you have to write it off in the year you bought it. For the big ticket items these are probably depreciated over several years so you get partial write offs in both years.