You can form a political party any time you want and never tell the FEC. This is in part because under the law creating the FEC, "political party" has a specialized meaning:
The term “political party” means an association, committee, or
organization which nominates a candidate for election to any Federal
office whose name appears on the election ballot as the candidate of
such association, committee, or organization.
Given that, the authorized (campaign) committee has to file a statement of organization within 10 days of designation under section 30102(e)(1), and that has to be done within 15 days of the candidate becoming a candidate. The relevant regulations (11 CFR Part 102) do not suggest that there is any restriction on when this can be done.
The only thing that I can suggest is that they were thinking of state-level restrictions on getting your name on the ballot.