This is a fun little comic, but it's pretty misleading. The USSR was certainly
whooping the US at the beginning of the space race, but they fell behind
in the 60's and there are many achievements by the US that they simply
never equaled. It also leaves out a lot of US firsts, like the first rendezvous in space.

The USSR only beat the US to the "man in space" by a few weeks, and unlike
Alan Sheppard, Yuri Gagarin did not actually control his craft at all and
didn't even land with it (a fact the USSR hid because it violates the rules
on aeronautics records).

The first woman in space is a rather weak argument since it's not a real
demonstration of equality, it was done purely for propaganda. Women
weren't allowed to be cosmonauts until 2 years after the US started
allowing women astronauts.

The mid-60s is where the USSR started to really fall behind, and some of
their last few firsts were accomplished in a rushed/slightly dangerous manner.

The US did the first docking of 2 craft in space. We started doing missions
long enough to do actual work. We did EVAs where actual work was done.

The US launched the first craft that was capable of changing it's orbit.

We orbited the moon first.

We sent more probes, farther than the USSR did.

etc etc...so yes...we won the space race in the end, but the Soviet program
was/is impressive nonetheless.