I am using Aws Lex for constructing chatbots. I had a scenario where I need to have welcome message initially without user input so that I can give a direction to the user in my chatbot.
You need to work that scenario using API call to start a context with your user.
You can follow these steps:

You need to create an Intent called AutoWelcomeMessage.
Create a Slot type with only one value i.e: HelloMe.
Create an Utterances HelloMessage.
Create a Slot as follow: Required, name: answer, Slot Type: HelloMe, Prompt: 'AutoWelcomePrompt'.
Pick Amazon Lambda for your Fulfillment that will send a response to your user. I.e:

Hello user, may I help? (Here the user will enter another Intent and your Bot will respond).
Now, start a conversation with your User, just call via API your Lex Bot and send an intention with Intent AutoWelcomeMessage, that call starts a context with your Lex Bot and the fulfillment will execute your Lambda.
How to get welcome messages in AWS Lex (lambda in Python)?