Does putting salt first make it easier for attacker to bruteforce the hash?

Many recommendations for storing passwords recommend hash(salt + password) rather than hash(password + salt).

Doesn’t putting the salt first make it much faster for the attacker to bruteforce the password, because they can precompute the state of the hashing function with the bytes of the salt, and then each time of their billions and trillions attempts they only need to finish calculating the hash using the bytes of the password.

In other words, each bruteforce iteration needs to calculate only the hash of the password intermediateHashState(password) instead of the whole hash(salt + password).

And if the salt was placed after the password, the attacker wouldn’t have this shortcut.

Does this advantage exist and is it significant?