I am always wondering this question. Of course from the computer science point of view, nothing is really random. You have a random function which may use system timestamp as a seed, or combination of mac address, computer architecture etc. So if I try to generate the bitcoin address using the similar conditions that Satoshi once had, maybe I can generate his address with a larger probability and may succeed one day, and get his lost treasure, lol. Though sounds not easy, but it is still possible, right?
You will never successfully generate Satoshi's addresses besides you need the wallet private key not the public address. It's not possible. A Bitcoin address is effectively (not truly) random although it's derived using a 160-bit hash of the public portion of a public/private ECDSA keypair. Using public-key cryptography, you can "sign" data with your private key and anyone who knows your public key can verify that the signature is valid.
How to create Bitcoin Address
Take a private ECDSA key
Take the corresponding public key generated with the ECDSA key (65 bytes, 1 byte 0x04, 32 bytes corresponding to X coordinate, 32 bytes corresponding to Y coordinate)
Perform SHA-256 hashing on the public key
Perform RIPEMD-160 hashing on the result of SHA-256
Add version byte in front of RIPEMD-160 hash (0x00 for Main Network)
Perform SHA-256 hash on the extended RIPEMD-160 result
Perform SHA-256 hash on the result of the previous SHA-256 hash
Take the first 4 bytes of the second SHA-256 hash. This is the address checksum.
Add the 4 checksum bytes from the end of extended RIPEMD-160 hash. This is the 25-byte binary Bitcoin Address.
Convert the result from a byte string into a base58 string using Base58Check encoding. This is the most commonly used Bitcoin Address format.
Bitcoin addresses are the pubkeyhash (not pubkey) plus version and checksum information, encoded in base 58.
Bitcoin address = version + RIPEMD-160(SHA-256( Public Key )) + checksum
This is not the point and the question is not about it.
If you try to randomly generate a key, then it is impossible (or virtually impossible). But the key pair is not generated completely random. It uses a random number generator which depends on the seeds. So with these clues it will not be completely random any more.