I have NEVER heard about any site needing 2 or even up to 5 minutes to accept any live bet. Within seconds the odds can change, I am 100% sure the odds changed several times in this 2 minute window, not only because things happened on the pitch but also because other people are placing bets which moves the line.
Pre game ok, I have seen sites that took some more seconds than usual to accept a bet, but pre game it doesn't matter. Live MUST be accepted within let's say 10 seconds, otherwise it's not really "live betting".