First sea launch ballistic missile
The US was more interested in Bombers than missiles. You can put more on them and they were more accurate.
First Satellite (Sputnik)
Only because of Politics. von Braun's ABMA was ready to launch a satelite in 1955 but were denied the opportunity (in fact banned from even attempting it) until 1957 when they threatened to resign if not allowed too.
First Animal (Dog)
But they weren't able to recover it.
First Human (Yuri Gagarin)
The craft wasn't able to soft land however and he had bail out before the capsule crashed.
First Woman (Lt. Valentina Tereshokva)
List padding for the most part. Man, Woman, no difference really as far as the rocket cares.
First Spacewalk Male (Alexei Leonov)
Only by risking his life. The Soviets didn't do a second spacewalk for 5 years until after the US had started Apollo.
First Spacewalk Female (Svetlana Savitskaya)
List padding. Man\Woman, no difference to the spacesuit.
First image Moon's far side
Done in 1959, the US had already launched 3 missions to do this in 1958, but they failed.
First robotic soft landing on Moon
First Lunar Orbit of robotic spacecraft
Also list padding, it was the same craft.
First artificial Martian satellite
First soft landing on Mars and first data returned (ok it screwed up after a few seconds because of dust storm but it did land an started transmitting data )
Again list padding. On top of that, both missions were a failure. The US's first attempts were total successes. Mariner 9, Viking 1 and 2
First robotic return sample to Earth from Moon (Luna 24)
The US never did a robotic return sample, they used people and still beat the Soviets. It was Luna 16 anyways.
First spacecraft to land on Venus and return data (Venera 7)
The Soviets did a major program to study Venus while the US was concentrating on sending men to the moon. The US didn't switch focus to Venus until after their Mars' program in 1978/9 when they sent Pioneer and landed four probes from it.
First Space Station
Again, while the US put nearly all their resourses getting to the Moon, the Soviets split theirs, sending robots to Venus and Mars, build a space station and trying to get to the moon. Different approaches resulted in different things. On top of that the Soviets had a "First at any cost" attitude, the US didn't.
Longest orbiting and habited station
The US has never really been interested in stations. They had a slight fling with Skylab and now with the ISS but it's never been a piority.
Longest in-space record for an individual human
Set because the pick up rocket couldn't make it to pick them up.
First Space tourist ( American Dennis Tito )
First Space Commercial shot from space for a Japanese drink maker
NASA simply isn't interested in space tourist and commercialism. Russia needs the money and will do anything because their space program is almost broke.
Of course none of the US firsts are mentioned, nor the US successes matched to the Soviet/Russian ones. The US space record is nowhere near rivaled by the Soviet one.
Here's my list and you'll note it's not complete, but it is longer without the padding (I could have added flybys past Neptune, and Uranus.)
1) First satellite to enter Van Allen Belt (Explorer 1)
2) First television weather satellite (Tiros 1)
3) First communications satellite (Echo 1)
4) First probe to study the Sun (Pioneer 5)
5) First manned spacecraft to successfully soft land (Freedom 7)
6) First successful probe to Venus (Mariner 2)
7) First satellite in polar orbit (Nimbus 1)
8) First commercial communications satellite in geosynchronous orbit (Intelsat 1)
9) First chemical analysis of lunar soil (Surveyor 5)
10) First robotic lander to lift off from moon surface (Surveyor 6)
11) First successful Mars Probe (Mariner 4)
12) First manned spacecraft rendezvous (Gemini 6-7)
13) First docking with a seperately launched target vehicle (Gemini 8)
14) First manned mission into Van Allen belts. (Gemini 10)
15) First teethering of two Spacecraft in orbit. (Gemini 11)
16) First manned flight round the Moon (Apollo 8)
17) First EVA between two space vehicles (Apollo 9)
18) First manned landing on Moon (Apollo 11)
19) First rover on the Moon (Apollo 15)
20) First successful lander on Mars (Viking 1)
21) First robotic probe to Jupiter (Voyager 1)
22) First robotic probe to Saturn and beyond (Voyager 2)
23) First reusable Spacecraft (Space Shuttle Columbia)
24) First space telescope (Hubble)
25) First Jupiter Orbiter (Galileo)
26) First Robotic Mars Rover (Pathfinder)
27) First Saturn Orbiter (Cassini)