Haven't been able to find an answer to this question. If an LLC is formed in October 2020 when I file taxes in April 2021 for the year 2020 can I claim the entire year expenses for the business in 2020 with the receipts I have or can I just use the expenses/receipts from October 2020 to Dec 2020?
You will not find a place to enter the date of LLC filing on Schedule C (or appropriate business tax form). What you will find are fields to enter valid business expenses for the year. Whether or not the business entity is an LLC or not is immaterial. If expenses are valid for the business in the tax year they will be allowed.
If you are the sole owner of the LLC and it does not elect to be taxed as a corporation, the LLC is a "disregarded entity" for income tax purposes, and all of your receipts and expenses for the business are reported on Schedule C.
If the business was a general partnership with multiple owners, and an LLC is formed with the same owners, you could file form 1065 partially for the pre- and post-LLC operations, but if you filed a single form 1065 with the entire year's results and the allocation of profits and losses were the same, it would not change the tax liability of any of the general partners.
If the business was anything other than a corporation prior to forming an LLC and the LLC elected to be treated as a corporation (most often as an S-corporation) upon formation, then you would need one set of tax returns up until its formation and a Form 1120 for the remainder of the year.
Likewise, if the business was a sole proprietorship prior to the LLC and had multiple owners after formation two returns would be needed.