in the first lines of the play, they are referred to as the "star-crossed lovers," meaning they were fated to meet and fall helplessly in love. And the action he creates transpires over a handful of days; at the end of these few days, Romeo and Juliet are willing to die for each other. Thus, there does seem to be some credence for the "love at first sight" analysis.
Romeo certainly proclaims his love for Juliet as soon as he beholds her:
Did my heart love till now? Forswear it, sight!
For I ne’er saw true beauty till this night.
He immediately forgets his misery over Rosaline, which has plagued him for the entire play thus far, and becomes much more hopeful with this immediate change in demeanor. When he finds out that Juliet is a Capulet, he bemoans, "My life is my foe’s debt"