We certainly can and do believe unto salvation. In John 3:15,16,18; 5:24; 6:29,40,47; 11:25,26 What is the ONE requirement that Jesus mentions in each of these passages of scripture? BELIEVES "apart from additions or modifications." In Acts 10:43, we read that whoever BELIEVES in Him "apart from additions or modification" shall receive remission of sins. In Acts 13:39 we read that all who BELIEVE "apart from additions or modifications" are justified from all things.. In Acts 16:30-31, in response to the question, "what must I do to be saved?" The answer is BELIEVE on/in the Lord Jesus Christ "apart from additions or modifications" and you will be saved. Romans 1:16 we read that the gospel of Christ is the power of God unto salvation to everyone that BELIEVES.. "apart from additions or modifications." So belief is not merely the 1st step.
In regards to the Ethiopian eunuch in Acts 8, after Philip preached Jesus to him, the eunuch asked what hinders him from being baptized? Philip said, If you BELIEVE with all your heart, you may. And he answered and said, I BELIEVE that Jesus Christ is the Son of God. (Also see John 20:31) Water baptism "follows" believing unto salvation, just as it did in Acts 10:43-47.
Belief alone means everything. Mark 16:16 ..but he who does not believe will be condemned. John 3:18 - He who believes in Him is not condemned; but he who does not believe is condemned already, because he has not believed in the name of the only begotten Son of God. In James 2:19, we see that the demons believe "mental assent" that "there is one God," but they do not believe in/have faith in/trust in/reliance in Jesus Christ for salvation. In other words, they do not believe on/in the Lord Jesus Christ (Acts 16:31) and are not saved. Their trust and reliance is in Satan, as demonstrated by their rebellion in heaven and continuous evil works.
Once again, Mark 16:16 - He who believes and is baptized will be saved (general cases without making a qualification for the unusual case of someone who believes but is not baptized) but he who does not believe will be condemned. The omission of baptized with "does not believe" shows that Jesus does not make baptism absolutely necessary for salvation. Condemnation rests on unbelief, not on a lack of baptism. So salvation rests on belief. *NOWHERE does the Bible say "baptized or condemned."
Belief and baptism are not inextricably tied together and they are not dependent on another. Believing is not baptism and we believe prior to receiving water baptism and we are saved the moment we believe in Christ unto salvation prior to receiving water baptism. Christ is the object of our belief in receiving salvation and to say that believing alone is insufficient to save us is to say that Christ is insufficient to save us. Christ's finished work of redemption is sufficient and complete to save believers. (Romans 3:24-28) No supplements needed. Salvation is signified, but is not procured in the waters of baptism.