I have a lot of timelines either by alone or by group similar to your specifications in terms of goal laying around this board, but this time I'm in for a new shift by taking up the mantles of abandoned TL "
The Stars Above: An Alternate Space Race".
1955: The planning for the upcoming International Geophysical Year was in full swing. President Eisenhower had just ordered the formation of a committee to decide on which proposal to fund for the IGY satellite project, as part of the United States' contribution to the international effort. Headed by Homer J. Stewart of JPL, the committee also held two representatives each from the Army, Navy, and Air Force, as well as two men selected by Assistant Secretary of Defense Donald Quarles: Joseph Kaplan, head of the American IGY committee, and William Pickering, the director of JPL. Out of the three proposals, Project Orbiter had been selected to launch America's first satellite.(This is the POD. OTL, Richard Porter got appointed instead of Pickering. The same Richard Porter who helped develop the Project Vanguard proposal in the first place. No wonder it got selected over Project Orbiter)
1956: On August 12th, after several test launches in the preceding months a Jupiter type rocket lofted Explorer I into space and into the history books.
1957: More Explorer satellites were launched and the Van Allen belt were discovered. NASA is formed while the Soviet Union launched a Sputnik I much bigger than OTL. Sputnik 2 were launched in November 3 carrying Laika the dog.
1958: Pioneer 1, 2 and 3 flew by the Moon and into heliocentric orbit, however the cameras failed to capture the image of lunar far side.
1959: Luna 1, 2 and 3 goes like OTL. NASA begins preparations for manned spaceflight program.
1961: Alan Shepard became the first man in space on March 24th, but however he was beaten by Yuri Gagarin into orbit on April 12th. After Kennedy made the pledge to go for the moon, the Soviet Union immediately responded in kind and approved the then secret N1 moon rocket project.
1962: John Glenn became the first American in orbit.
1963: Soviet cosmonaut Valentina Tereshkova became the first woman in space.
1964: Soviet's Zond 2 Mars probe succeeded TTL.
1965: Alexei Leonov conducts the first spacewalk.
1966: Irina Solovyova is the first woman to spacewalk in the Voskhod 4 mission.
1967: Soyuz 1 ended up successful, but Apollo 1 fire happened as OTL.
1968: Apollo 8, and Yuri Gagarin didn't die in the plane crash.
1969: On May 17th Vladimir Komarov and Victor Gorbatko became the first Soviet cosmonauts to orbit the Moon in a Soyuz 7K-LOK spacecraft. Neil Armstrong became the first man on the Moon in Apollo 11 mission on July 20th. On August 4th the Soviets reciprocated by sending a manned mission with cosmonauts Alexei Leonov and Oleg Makarov to Mare Serenitatis of the Moon. The Space Race has become a Space Marathon. Amidst the panic of losing the marathon President Nixon decides to keep and expand the Apollo Program to include moon bases into the scope. Chinese Dong Fang Hong I became the first Asian satellite.
1970: Apollo 13 didn't encounter failures at all. Irina Solovyova became the first woman on the Moon.
1971: Both Mariner 8 and Mars 2 arrived at the target planet, this time the Mars 2 lander is successful. Later on Mars 3's rover became the first to do so on the planet. Salyut 1 space station is launched.
1972: Apollo 20 touched down at Copernicus Crater. Meanwhile in Moscow a plan is approved to upstage the Americans once again with an automated Mars sample return mission.
1973: Skylab I is lofted to orbit.
1974: Launch of NASA Mariner 10 to Venus and Mercury. A LESA moon base is set up at the Mare Insularum.
1975: Nominal space detente as US and USSR conducted Apollo-Soyuz test project.
1976: First US Mars lander Viking I arrives on Mars.
1977: Launch of the Voyager probes.
1979: Soviet Mars 5M sample return mission commences, which would arrive at the planet a year later.
1982: The Soviet Mars sample return capsule arrived at Earth.
1991: Soviet Union dissolves and transformed into the Russian Federation.
1993: Russian constitutional crisis, also Yuri Gagarin emigrated to the U.S. and settled down in Houston on a permanent residence basis.
1996: Mars 96 was launched to Mars successfully.
2001: 9/11 attacks.
2008: Start of the Great Recession. Barack Obama elected president
2009: H1N1 pandemic.
2010: An improved International Space Station with a rotating habitat is completed by this time.
2011: Arab Spring.
2014: Start of the Ukrainian conflict after a revolution toppled Yanukovych
2016: Donald Trump won the presidential election as OTL.
2019: Hong Kong protests.
2020: COVID-19 pandemic. Yuri Gagarin contracted it after travelling to a conference in Houston. He eventually succumbed to the virus causing far more widespread grief worldwide.