When do cycling betting odds show up?
For the major races of the year: Giro d'Italia, Tour de France, Paris/Roubaix, and Tour of Flanders you can expect the odds to appear earlier in the calendar year, even in December of the previous year. This may be an ideal time to get deals on riders you expect to win, but it also ties up your funds for a long period of time. And because of the latter we wouldn't recommend betting early in the year unless you think the rider you want to back is going to shine extremely brightly in the earlier season races and their odds will plummet.
Say you knew in 2023 that Jay Vine was going to be stellar early in the season and win the Tour of Australia. Placing a bet on him to win the Giro d'Italia for 2023 before he opened his standout season would make sense. The odds of him winning the Giro have changed dramatically after his well deserved win at the Tour of Australia.
But otherwise you're parking your money in what is basically worse than a savings account.
For smaller one-day races the odds will typically appear 2-3 days before the race, so pay attention. Betting houses may also offer more options closer to the date of the race. So while they may have 'Outright Winner' odds a week out from the race, they may offer 'Top 4' or 'Top 10' odds the day before the race. This is quite common for monuments like Milan San Remo so it's worth checking back every so often.
For multi-day races (2.X) like the Tour de France or Volta Catalunya they'll have the 'Outright Winner' odds up usually a few days out and then each stage's 'Outright winner' will appear ~16 hours before the race (or a few hours after the previous stage finished). Head to head match up odds (whether rider X will beat a similar calibre competitor Y) will also be generally offered for stages at the same time.