You can move up with a proof of time from a 10k or longer run. It does have to be fairly recent (within last 1-1.5 years roughly), or you can run one beforehand, provided it's completed and you submit your time ahead of the deadline for proof submissions. If you do not have a proof of time, you will be placed in one of the last corrals behind those who did submit proof of time.
More specific information about how recent the results have to be and when the deadline for submitting results should be available on the runDisney event page.