The order of events in the Leroux novel can be a bit confusing due to the “puzzle“ style of the narrative, so I‘ve tried and listed everything with a chronological indication in the (hopefully) correct order and timeframe. Piecing everything together, it is quite amazing how quickly things happened…
Beginning of November, possibly late October ("a good 3 months" before Christine‘s first disappearance): Erik and Christine meet, Erik starts teaching Christine. Talk of the “Opera Ghost” also arises “several months” before the gala, so probably around the same time.
January 10: Gala night featuring Christine, departure of Debienne and Poligny, Buquet’s body is found, Moncharmin and Richard learn about the ghost. Raoul hears Erik‘s voice in Christine’s dressing room.
The anniversary of Christine's father's death and her trip to Perros take place at some point later in January.
January 25: a note from the opera ghost arrives, claiming Box 5. M and R reserve Box 5 for Debienne and Poligny, so it remains empty.
January 26: Thank-you note from the ghost arrives, Box 5 sold to the public, occupants thrown out. Erik‘s note also states that he will write to them soon concerning the payment of his salary.
January 27: Mme Giry interrogated
The Saturday after: Faust performance where chandelier falls. Erik brings Christine to his house, where she stays for 2 weeks.
2 weeks later (mid-February): Christine and Erik go to the Masked Ball. Christine meets Raoul and later returns to Erik for the night. He gives her the wedding ring and she returns home the next morning.
Next day: Raoul visits Christine at home and sees the gold ring.
Next day: Raoul sees Christine at the Opera and tells her that he will be leaving in 3 or 4 weeks for the North Pole. The engagement game begins.
1 week later: Christine runs off to Erik.
2 days later: Christine reappears in “La Juive”
The following days are not stated, but it seems to be about another week, possibly, until the rooftop scene. Maximum duration of the entire engagement episode: 3-4 weeks, so no later than mid-march. The evening of Christine‘s abduction coincides with the payment of the Opera Ghost‘s monthly salary.
Rooftop scene evening: Raoul shoots Erik on the balcony. Raoul and Philippe quarrel.
Next day: The supposed engagement of Raoul and Christine is announced in the newspaper. Raoul prepares elopement and goes to the opera house at 9 pm. Christine is abducted from the stage. Erik sets her an ultimatum until 11 pm the following night (24 hours). Second payment collected. Past midnight, Raoul and the Persian go off in search of Christine and fall into the torture chamber.
Next day, 11 pm: Ultimatum runs out. Christine turns scorpion. Raoul and the Persian almost drown, but are recovered by Erik and Christine.
The Persian is delivered back to his apartment probably 1-2 days later, depending on how long he slept. Erik lets Christine and Raoul go.
Shortly after: Erik comes to visit the Persian.
3 weeks later: Erik dies (end of March to possibly mid-April).
So Erik met Christine (and most likely started masquerading as the opera ghost) at the beginning of November, and died the following spring at the end of march, maybe mid-April at the latest. This means that the entire plot, from Erik‘s and Christine’s first meeting to his death, spans only 5 to 5 ½ months in total. Therefore, they knew each other for a much shorter time than commonly assumed, especially within the context of the ALW musical.
