There is some evidence that an absolutist dictatorship might be better positioned to pull off a large project like a Mars mission than a typical 20th century democracy. Historically, tyrannies have been very successful with large scale, major projects, even ones at the edge of technological capability.
In ancient Egypt, the pyramids represented incredible investments of time, labor, and highly skilled engineering prowess, and they were built under the auspices of absolutist "god-emperors". similarly in ancient China, both the famous Great Wall, and the far more interesting world exploration project of the 1400s happened under absolute emperors willing to kill those who did not obey. In the case of the exploration project, a lot of comparisons can be made between an exploration fleet of the size and complexity developed at that time and a nation the size of the USA putting together a Mars mission now. We are talking about bleeding edge technology, a large crew to man the mission, unknown exploration in a dangerous environment, and ships larger than had ever been built in human history. Even the more well known Spanish and Portugese exploration efforts a few decades later were conducted under the authority of absolute monarchs who could gamble significant percentages of their nations' total budgets on very risky, high tech exploration efforts.
In more modern times, the Nazi regime not only developed: rocket powered fighter planes, jet fighters, ballistic missiles, assault rifles, and tanks with hybrid propulsion systems while their opponents were still mostly relying on biplanes, they were also on the verge of developing an atomic bomb, and would likely have done so given only a couple more years. Famously, the USSR, after a totalitarian regime took power and drove millions of people into slave camps in Siberia was able to radically upgrade it's national infrastructure and technological/industrial base. The Soviet Union, right up until the end of it's tyranny, was able to make MORE rockets than the USA, BIGGER rockets than the USA, and in some cases more sophisticated rockets too. They did fall behind in innovation over the long term, especially with the microchip revolution in America, but the USSR was always able to throw large amounts of resources at massive, high tech projects with a good deal of success.
The failure of these systems usually stems not from their ability to win a "space race", launch a huge battleship or create the world's largest gun. Generally, their failure comes as a result of the misallocation of resources to such grand projects (like your Mars mission) while common people have to stand in bread lines, wait years for an automobile, sometimes starve, and get more and more unhappy because they are assigned a job for life whether they like it or not.
There is no real contradiction between technological advancement and tyranny. Engineering may have a creative side, but engineers under extremely oppressive regimes throughout history have proven capable of developing some VERY impressive advances. Obviously, if your regime is under such pressure that it resorts to assembling V-2 missiles in underground tunnels with slave labor on loan from a concentration camp (as the Nazis were compelled to do) the quality of work will degrade to such a point that there will be more explosions and crashes than successful launches. This may explain some things about the peculiar North Korean nuclear weapon program with it's numerous, strange failures.