(Matthew 23:13)
That's interesting because a Mormon friend once discussed this very thing. You likely know that hundreds of billions of people have been born and died outside God's Old Testament covenant with Abraham and without ever hearing of or knowing Jesus Christ. Are those people, per your beliefs, barred from Heaven?
Also, as a clarifier, what's your definition of Heaven? Is it an actual place?
As a place, yes.
The simplest definition would be the place where the greatest degree of God's glory dwells. Indeed, He's omnipresent; fortunately for us, much of that glory is shielded from us, lest we be even more "undone" than Isaiah was in His Holy Presence (see Isaiah 6).
Btw, given the day it is...Here's a relevant comment on that:
Reformed pastor R.C. Sproul has at times describes various radio programs of the 1940's…The scariest of all scary (allegedly; certainly well before my time) was a radio program called: Inner Sanctum...
Sproul points out how the program's intro would bring awe, dread, fear. What does "Inner Sanctum" mean? Within the Holy.
Anyway, a place where Heavenly Father doesn't dwell is NOT heaven...
Therefore, Mormonism attempts to skirt that reality by claiming He doesn't even dwell in most of Mormonism's "ghettos".