Amazon Connect get customer input takes too long to initialize Amazon Lex bot

If the Lex bot is not used for a period longer than 24h, the first time is initialize after this it will suffer a cold start (in this case it will take some seconds to reply). If cold start is a problem, you may want to pre warm the bot regularly, (you can use Eventbridge + lambda for this. You can use for example the Lex PutSession API to start a new session and pre warm the bot).

If cold start is not the problem (so you have active traffic at least every 24h), you should check the timeout options of Lex and the time out options for the get customer input block. You can try to limit the response times expected to a certain number of seconds and see if that solve the problem.