The Moment of Prescience spell grants its caster a large one-time bonus on certain types of rolls and checks. The restrictions on the rolls it can be applied to are:
...any single attack roll, opposed ability or skill check, or saving throw.
An initiative check is explicitly a Dexterity check (and therefore an ability check):
An initiative check is a Dexterity check.
It also behaves in some ways as an opposed check:
An opposed check is a check whose success or failure is determined by comparing the check result to another character’s check result.
However, initiative checks are not explicitly called out as being opposed checks, and some of the wording for opposed checks does not fit (because initiative checks don't exactly succeed or fail):
In an opposed check, the higher result succeeds, while the lower result fails. In case of a tie, the higher skill modifier wins.
Can the bonus from Moment of Prescience be applied to an initiative check?