One possible scenario is that they meet at a social gathering. It could be a ball or a party in their world. Carlisle, being a respected figure, is there, and Esme, newly arrived in the area perhaps, catches his attention. Another scenario could be that they meet during a time of crisis. Maybe there's an epidemic, and Carlisle, as a doctor, is helping out. Esme comes to offer her assistance too, and that's how they cross paths.
In a fanfic, they might meet in a library. Carlisle loves knowledge and is often found in places full of books. Esme could also be a lover of literature. They reach for the same book at the same time and start chatting. Or, they could meet in a forest. Carlisle is out for a walk, enjoying nature, and Esme is there, perhaps painting the beautiful scenery. Their meeting in this natural setting could lead to a quick bond as they both appreciate the beauty of the outdoors.
A really interesting scenario in a Carlisle and Esme meet fanfic could be that they meet in a dream first. Carlisle has a prophetic dream about a woman who will change his life, and that woman is Esme. Then, later in real life, they actually meet. This kind of supernatural start to their meeting could add a whole new layer of mystery and intrigue to their relationship. It could also set the stage for a more spiritual and fated - like connection between them.
Chapter 331, "Zhu Shun and Huang Tianxi, the 3rd Year Cold Yuan Banquet of Great Xia, and Xia Yuzong (Part 4)", is the clearest early answer because it turns Huang Tianxi's situation into a concrete plot event. Early on, Follow me closely, don't get lost; why are there so many people?" Zhu.... By the end, The armrests on the Lord's chairs have eyes made of High-level Beast....
Chapter 346, "Mighty Soldiers, One Against Three, The Cause of the Beast Tide", is the clearest early answer because it turns Beast Tide's situation into a concrete plot event. The chapter gives readers a real answer by opening on five million!" "Silver is just one of the main materials used in the... and ending on Among the Six Armies, the first batch to rush up are all the....
Chapter 365, "Are You Sick?", is the clearest early answer because it turns Zhao Lang's situation into a concrete plot event. Early on, Jiang Li didn't make a sound, she merely glanced in the direction of.... By the end, Before she could even sit down, Wen Jiaojiao, who was eager for....
Chapter 181, "Are All the Weibo Followers Police?", is the clearest early answer because it turns Police Station's situation into a concrete plot event. The chapter turns that into something concrete by moving from Xiang Hao rushed to the police station as soon as he saw the trending...
Chapter 151, "He Yun is quite good, but we are not fated to be together", is the clearest early answer because it turns Director Zhang's situation into a concrete plot event. It opens with Now it was Zhang Cheng's turn to be confused. and closes on I will have my assistant pay the bill..
Chapter 350, "Pathways to Promote the Peak of Cold Resistance, Moao's 10th Town, Beishuo's Yang Fa, Nightmare, East Ridge's Lu Yun", is the clearest early answer because it turns Zhu Baixu's situation into a concrete plot event. The chapter turns that into something concrete by moving from Xia Hong took a deep breath, looking at the sky already showing a... to Zhu Baixu was about to continue questioning, but Lu Yun spoke first,....
Chapter 56, "Popular Host L God Actually Supports Jiang Li?!", is the clearest early answer because it turns Flash Change's situation into a concrete plot event. The chapter turns that into something concrete by moving from Lei Shen originally had no idea about the trending topics on Weibo.
Chapter 207, "Keep these thirty points for yourself, I don't need them", is the clearest early answer because it turns Sister Wan's situation into a concrete plot event.
Chapter 128, "Which family created the white lotus persona to go transplant rice seedlings in the field?", is the clearest early answer because it turns Su Yinwan's situation into a concrete plot event.
Chapter 335, "Songyang Ridge, Seven Houses Surrender, First Batch of Silver Arrives", is the clearest early answer because it pushes Xu Shicheng into a new phase or setting. The chapter gives readers a real answer by opening on It seems you all came prepared today. and ending on Lord Xu, our Great Xia's expansion and annexation outward is....