F-104A will do 10,000ft from brakes off in under 42 seconds. It set this record in 1958. Just short of 30,000ft in 90 secs.
And the MiG is quicker.
A modern fighter, say the Flanker which admitedly has become the measure for all other types to compare, in 55 seconds it does about 40,000ft from brakes off. In 59 seconds it'll do the very same thing with four R-73 and two R-27R slung on pylons. It set these records in 1987/88.
F-16s are tricky vicky. Every production block is a completely different animal. Say we talk a Block 15 well it's got phenomenal initial rates and acceleration but basically isn't really much different to a MiG-23 on those angles, it has about ten times their manoeuvrability and SA though. Get some air under your wings and the MiG will easily outspeed one on any test you care to make, climb, acceleration, airspeed, time to whatever.
But you get something like a Block 50/52 and what you're talking about is something that performs pretty much the same at 25000 than it does at sea level and that's the edge the modern Vipers have.
Still a bit restricted on spools when you're dealing with the big daddies like the Foxhound, which has almost 10% more thrust at 30,000 supersonic than it does at sea level static, it's a scary beasty that actually gets quicker the higher you go and not just because of calculus, so whilst you're climbing and running out of steam it's saying oh yeah baby, come get some, keep coming.
Like what was said though mechanical torque is good for instantaneous acceleration at low speed/alt and those early turbojets needed lots of spooling, meanwhile genuine engine management was almost non-existent, you had to "handle" them, watch airflow overspeeding, pressure temperatures, material limitations, things like that.
When proper management systems appeared and you could finally treat jet engines like four strokes, they got much quicker again, but this didn't really happen too well until the 80s.