I think this depends on what we mean by “being selfless.” And no single word or phrase fully captures the meaning of life.
But increasing realization of the meaning of life is fundamentally related to love and spirituality and that unfoldment makes a person less egocentric and more truly interested in helping others. This takes them beyond the narrow sense of self in which most people live and we could call that being more selfless. But selfless in this sense is really also an expanded sense of self, so it is the gaining of a greater and wider sense of identity that includes the lesser one. This we call the higher self and in that consciousness one feels an ever deeping sense of unity and responsibility with and toward others and toward life as whole.
“…but I was a vastness somehow, that in no way contradicted or conflicted with my limited individuality… I was both my individual self and in some greater way, ‘I’ was also everything.”
The Sound of Light, Irina Starr
“Thus it is, when the spirit comes to realize
New wings grow, and the surrounding air sings at
The pathway of light is revealed to the amazed sight.
And the mind’s resolution builds the steps
of the temple of the One Truth.”
Leaves of Morya’s Garden, I: The Call, par 355