I want to say on social media that I am blessed to have my daughter, but I am not religious and find it awkward when people respond saying that they are sending prayers my way. I appreciate the sentiment, but I'd still like a non-religious word that holds a similar connotation.
From a religious point of view, being blessed has two parts. The first part is to have been endowed with divine favor. The second part is to be joyful for having received the blessing.
No doubt that as a new father you feel any one of these, from the second part: overjoyed, jubilant, exultant, elated, gleeful, delighted, or wonderful. None of these attributes your feeling to any outside influence. With these words, a thesaurus can be used to give you additional ideas.
My favourite is "privileged."
I feel this is the closest in connotation.
[Extremely] fortunate, [awfully/terribly] lucky.
May be, "Gifted"!
And, like the other answerer has suggested "fortunate" would fit in too.