You are simply incorrect that the USPS needs to pay for an employee's pension on day one. They contribute according to a vesting schedule, same as any private sector company not grandfathered.
It's only in their projections that they must include full costs. Unlike many other agencies, the USPS can't tell Congress that a program will cost $X over the next 10 years, where $X excludes the cost of employee pensions.
You are probably misunderstanding the pre-funding schedule. Beginning in 2006, the USPS was obligated to make pre-funding payments with the goal of fully pre-funding 75 years worth of pensions by 2017. See the linked WaPo article, which explicitly states "Congress passed a statute in 2006 requiring the early payment of 75 years worth of retiree benefits within 10 years. " (This is not the same as vesting, because the pre-funding obligation is not tied to the vesting of any particular group of beneficiaries' benefits.)
More specifically, see section 801, et. al., for the specific language of the Postal Accountability and Enhancement Act fo 2006 which creates the silly requirement.
According to the actual law, what must be fully funded is the "actuarial present value of all future benefits payable from the Fund." What this means is that if an employee's pension has 50% vested, their "future benefits payable from the Fund" are 50% of their pension. The USPS is then obligated to put 50% of the NPV of their pension into the fund by 2017.
It's explicitly stated 5 times it should comport with "generally accepted actuarial practices and principles", which rules out all the insanity people seem to be attributing to this law.
Is your claim that the postal service must pre-fund unvested benefits at the day the employee is hired? That is, is that how you think "future benefits payable" is being interpretted? Because what's definitely not true is that the postal service is being required to fund un-hired (or unborn) employees. See this article, which has quotes from the Congressional Research Service.
(c) Variance from minimum funding standards
(1) Waiver in case of business hardship
(A) In general
(i) an employer is (or in the case of a multiemployer plan, 10 percent or more of the number of employers contributing to or under the plan are) unable to satisfy the minimum funding standard for a plan year without temporary substantial business hardship (substantial business hardship in the case of a multiemployer plan), and
(ii) application of the standard would be adverse to the interests of plan participants in the aggregate,
the Secretary of the Treasury may, subject to subparagraph (C), waive the requirements of subsection (a) for such year with respect to all or any portion of the minimum funding standard. The Secretary of the Treasury shall not waive the minimum funding standard with respect to a plan for more than 3 of any 15 (5 of any 15 in the case of a multiemployer plan) consecutive plan years.