If willing to stand in line, there are two ticket offices nearby: at Piazza del Colosseo and Largo Salara Vecchia.
https://colosseo.it/sito/wp-content/uploads/2023/11/Biglietteria_Ticket-Office_Colosseum-scaled.jpg
I would plan to get there well before they open to reduce potential time standing around, and to be more sure of landing some of the tickets allocated for that day. Have your passports in hand and your entire party with you: tickets are nominative and will be checked against your personal info at the entrance.
https://colosseo.it/en/opening-times-and-tickets/
"Starting from the 18th October 2023 the Parco archeologico del Colosseo has arranged for the opening of an additional ticket office, located at Largo della Salara Vecchia, for the sale of admission tickets destined exclusively to individual non-mediated visitors, until daily availability is exhausted. The availability of tickets on sale at the ticket offices in Piazza del Colosseo and Largo Salara Vecchia will be doubled. Also as of the 18th October 2023, the obligation of nominative tickets will be extended to all types of tickets available on the sales website, at the call centre and at the physical ticket offices. Your proof of identity must be kept on hand at the Park entrances together with the purchased ticket. Please be advised in order to avoid queues forming."
The 2 offices mentioned above are official ticket sellers for this attraction, and the 24-hr Colosseum, Roman Forum and Palatine ticket is the least expensive available for purchase. It will not get you into the underground or arena sections of the Colosseum but any ticket involving the underground is very, very difficult to get, and you can see down into the uncovered parts from sections above so I wouldn't stress about it. I'm not even sure they sell tickets that include the underground at the on-site offices as you're not allowed access to that part without a tour or accompaniment of Coopculture staff.
https://colosseo.it/en/tickets/24h-colosseum-roman-forum-and-palatine/
You didn't mention the dates of your trip? Is it possible tickets just aren't on sale for those dates yet?
Must-sees? Entirely up to personal interest: Ancient Rome/archeology; art; Christian history and landmarks; architecture, etc.