No, it is not necessarily true that if a girl says "I love you" first, she loves the guy more than he loves her. Expressing love can vary greatly between individuals and can be influenced by several factors such as personality, communication style, cultural background, and personal experiences.
The timing of saying "I love you" can be different for each person, and it doesn't always indicate the depth of one's feelings. Some people might feel comfortable expressing their emotions earlier in a relationship, while others may take more time to open up emotionally. The timing of saying "I love you" should not be used as a sole indicator of who loves whom more.
Love is a complex and multifaceted emotion, and it's challenging to measure or compare it quantitatively. It's more important to focus on open and honest communication between partners, as well as the quality of the relationship and the emotional connection between them, rather than trying to assess who loves the other more based on arbitrary factors like who says "I love you" first.