Is it possible to obtain a clearance on the ground without having a void by time? Would ATC ever give you a clearance to say "yeah, just take off and we'll figure it out in the air"?
If you're flying through crowded airspace, it seems like an opportunity spend an extended time in a hold waiting for them to figure out where to slot you in.
Yes. But from an uncontrolled, aka non towered airport, which the OP was at, you must get something other than just the clearance.
4−3−4. DEPARTURE RELEASE, HOLD FOR RELEASE, RELEASE TIMES, DEPARTURE
RESTRICTIONS, AND CLEARANCE VOID TIMES
Assign departure restrictions, clearance void times, or release times to separate departures from other traffic or
to restrict or regulate the departure flow. Departures from an airport without an operating control tower must be
issued either a departure release, a hold for release, or a release time.
a. Departure Release. When conditions allow, release the aircraft as soon as possible.
PHRASEOLOGY−
To another controller,
(aircraft identification) RELEASED.
To a flight service specialist, or Flight Data Communication Specialist (FDCS).
ADVISE (aircraft identification) RELEASED FOR DEPARTURE.
To a pilot at an airport without an operating control tower,
(aircraft identification) RELEASED FOR DEPARTURE.
b. Hold For Release (HFR).
1. “Hold for release” instructions must be used to inform a pilot or a controller that a departure clearance
is not valid until additional instructions are received.
REFERENCE−
P/CG Term − Hold for Release.
2. When issuing hold for release instructions, include departure delay information.
PHRASEOLOGY−
(aircraft identification) HOLD FOR RELEASE, EXPECT (time in hours and/or minutes) DEPARTURE DELAY.
c. Release Times.
1. Release times must be issued to pilots when necessary to specify the earliest time an aircraft may depart.
NOTE−
A release time is a departure restriction issued to a pilot (either directly or through authorized relay) to separate a departing
aircraft from other traffic.
2. The facility issuing a release time to a pilot must issue a time check. A release time using a specified
number of minutes does not require a time check.
PHRASEOLOGY−
(aircraft identification) RELEASED FOR DEPARTURE AT (time in hours and/or minutes),
and if required,
IF NOT OFF BY (time), ADVISE (facility) NOT LATER THAN (time) OF INTENTIONS.
TIME (time in hours, minutes, and nearest quarter minute).
(aircraft identification) RELEASED FOR DEPARTURE IN (number of minutes) MINUTES
and if required,
IF NOT OFF IN (number of minutes) MINUTES, ADVISE (facility) OF INTENTIONS WITHIN (number of minutes)
MINUTES.