See https://www.irs.gov/retirement-plans/plan-sponsor/401k-resource-guide-plan-sponsors-starting-up-your-plan
"Effective date of plan. The plan may not be made effective earlier than the first day of the employer's tax year in which the plan was adopted. In other words, an employer may adopt the plan document on the last day of its tax year, with an effective date retroactive to the first day of that tax year, but not any earlier."
A CPA firm discusses the topic of Determining When a Business Starts for Tax Purposes
"When deciding to open a business, it is important to understand when a business has started for tax purposes. It is normal for a new business owner to misconstrue when the company is liable for taxes. In some cases, a business owner may believe that their company must only pay taxes when they start advertising or when the company draws in clients and begin to earn income. However, for tax purposes, the start date does not consider these factors.
Normally, the start date for a business is when the business is registered. This means that a company like an LLC or a partnership is responsible for paying taxes on the date they register with a particular state. Note, however, that it may be possible for a business to choose their start date.
Additionally, when registering a business with a state, a company is often required to also register with the IRS in order to receive an Employer Identification Number (EIN). A company’s EIN is used to identify the company for tax purposes.
It is important to note that the start date of a business can change depending on other factors. For example, under certain circumstances, the IRS may analyze a company’s activities to determine whether they are liable for taxes."
Taken together, these steps seem appropriate:
The starting point is for a business first to decide what will be its ongoing tax year.
Next the business should decide when its first tax year began.
Then the business can decide when the beginning and ending date it wants to have for its plan's ongoing plan year.
Finally, the business can decide on the beginning date of the first plan year - subject to the IRS comment above.
Once the first plan year is determined and if it is a short plan year, then the rules applicable to pro-rating limits over a short plan year come into play.