Why should Social Media managers begin the budgeting process for their social marketing program well before final budget numbers are settled?

Because there will likely be other projects that arise and it’s important to leave yourself enough time to complete a budget before the end of Q4.
So that you can get your budget requests in early so that your requests are prioritized over other teams.
Because social managers are often overwhelmed with tactics and campaigns at the end of the year.
Vacations around Thanksgiving and Christmas often make it difficult to get the data needed in time for final budget submissions.
To make the most persuasive and data-driven case possible for influencing how much will be awarded.