Suppose I have no idea about relativity and find an ancient spaceship that takes me to Proxima Centauri in just 1 year more than it takes light to make the trip (so some observer might say it took about 5 years).
Now from my point of view it only took 1 year (if it had been at light speed, the trip would have been instant). My new friends at Proxima Centauri also agree that they saw it take 1 year (the light from Earth when I left reached them just 1 year before they saw me arrive). None of us could perceive anything other than classical Newtonian mechanics happening.
Meanwhile others on Earth who never understood relativity would observe that my trip took 9 years and the photos I send to them upon my arrival show I only aged 1 year. They would be surprised.
Is this correct? Meaning for a naïve space traveler from Earth and like-minded observers at the destination, relativity wouldn't seem to set any speed limit?