BartK I did not show the second page of the score - it is essentially the same as page 1 but forte in dynamics. Pedal does make the sound quite more majestic in forte.
What confuses me a bit is the opening dynamics is piano. The pedal effect there seems to me more for legato than for resonance when playing soft? However I do feel in measure 4 the pedal makes the bass register quite a bit more sonorous even played soft.
One more question, if the goal is to make the sound more majestic, would pedal down before the opening note in measure one even better?
BTW although I am on a digital piano, I am using Pianoteq which models the pedal effect quite realistically.