You do not say if you are after booking a specific girl on the day, or are just after a same-day booking with whoever might be available that day. In either case, the surest way to make a same day booking is with an agency. They will tell you who they have available at the time you want, or what time your preferred girl is available. But you inevitably pay for this convenience.
There is little point in calling or texting a girl super-early before she starts work, or turns her phone on. Yours will be one of dozens of missed calls/messages that she will most likely ignore. Best bet is to call soon after she turns her phone on. Don't assume that because a girl has her green light on, that she has started work that day.
My preferred method is first to call. If the girl doesn't answer for some reason, then leave an SMS message. If the girl doesn't answer within a reasonable timescale, move on to the next. If you only have a limited window, then try contacting multiple girls simultaneously. But don't make it obvious that you are doing so, by copying a generic message, or by contacting girls working together, as they are unlikely to respond if they think they are wasting their time. And beware that contacting a girl and then going silent when she responds is likely to get you blacklisted as a timewaster if done more than once. And once you have made a confirmed booking, do not cancel it, as doing so will also quickly get you blacklisted.