We can say the drive flare emerges in a near-perfect collimated beam, so it's hard to spot from Earth...and when the Russians took a second look at the energy output and realized the Giant Death Laser it made they promptly shat a brick.

I notice the starship is supposed to have launched in 1963. Give the Russians a few months to freak out and organize a response...the project must have been insanely classified, only known to a few American politicians at the very top...obviously the Russian protest was lodged on December 22nd, 1963.