No.
Before the world even began, God foreordained that no one would enter Heaven w/o the shed blood of Jesus Christ applied to his credit.
Jesus, the Second Person of the Godhead, even volunteered to be the Savior of mankind.Adam, Noah, Joshua, David, Solomon, Isaiah, Malachi --- no one went to Heaven when they died.
Instead, the Old Testament saints went to Paradise, situated next to, but far removed from, Hell itself.
God (the Father) made sure that the first Person* to enter Heaven proper, would be His very own Son, bringing Paradise with Him.
* An exception to that would be the angels, who are classified as "persons", but not in the same sense that we are. They are not tripartite (three-in-one) beings like we are.