no they can't. the process that derives a public key from a private key is a mathematically irreversible process that only works in one direction (from private to public key).

to see it in action you can look at bitcoin's blockchain, each translation that has signature also has the public key in it and nobody has ever been able to reverse it as long as the private key was randomly selected. you can also look at the website SSL certificates when you visit a site with https, they usually also use the same cryptography scheme with their certificate being a public key.