The short answer to this question is; no. Jesus says in John 14:6, referring to Himself, “I am the way the truth and the life, no one comes to the Father except through me.” But it is important to realize why it has to be this way. You see, the whole reason we are separated from God in the first place is because we are sinners, in other words, we are people who do things we know we shouldn’t do. Because God is perfect and holy, it is impossible for him to be around sinful humans. God saw that this was a problem so he sent his son Jesus who lived a perfect life to die on our behalf. When Jesus died something amazing happened. In God’s eyes, all the sins that you and I have ever committed were transferred to Jesus. It’s kind of like if you are standing before a Traffic Judge and he says you are guilty of several speeding violations, but then turns around and pays for the ticket out of his own pocket. The Judge recognized that in order to be just, these wrongs needed to be corrected, but he also knew you couldn’t pay for them yourself. If we didn’t believe in Jesus, than there would be no payment made for our sins and those sins would keep us away from God. Belief in Jesus is more than just believing that a long time ago this guy named Jesus existed and actually lived (although that is an important part of it). It is also recognizing that we can’t get to Heaven on our own. Only through Jesus’ paying for our sins could we be allowed in.
There is another way we can look at this question in addition to what we discussed before. Imagine you are looking at it from God’s perspective. For this exercise we will have to stretch our imaginations, but if you bear with me you’ll see the point. Let’s pretend that one of your close friends stole a million dollars from you. He was then arrested and sentenced to life in prison. After some bargaining with the lawyers the Judge decides he’ll let your friend out of jail, if you allow your son to be beaten and jailed in his place. Now, you love this friend of yours more than anything so you decide to allow your son to be imprisoned and beaten on his behalf. So your friend is released from prison and your son taken in exchange. When your friend is released you are there waiting to meet him. However instead of walking up to you and greeting you with hug, he walks right past you and gives you a nasty look. For some unknown reason, he never wants to speak to you again. Not a “thank you” or a “why did you do that for me?” Nothing. He refuses to acknowledge the sacrifice you made and simply chooses to believe that it must have just been his lucky day. After such an enormous sacrifice by you, your friend flat out rejects you. How would you feel? Wouldn’t you want some recognition for the sacrifice you made? God feels the same way.