I want to connect to the database before my function start

Then you can run this function as a Task after supervisor(Repo, []) in your application.
Replace https://github.com/dersar00/friends/blob/master/lib/friends/application.ex with

defmodule Friends.Application do
  # See https://hexdocs.pm/elixir/Application.html
  # for more information on OTP Applications
  @moduledoc false

  use Application

  def start(_type, _args) do
    import Supervisor.Spec
    children = [
      supervisor(Friends.Repo, []),
      worker(Task, [&Friends.save/0], restart: :transient)
    ]

    # See https://hexdocs.pm/elixir/Supervisor.html
    # for other strategies and supported options
    opts = [strategy: :one_for_one, name: Friends.Supervisor]
    Supervisor.start_link(children, opts)
  end
end

Don’t forget to delete https://github.com/dersar00/friends/blob/master/lib/friends.ex#L10

My architecture is:
I build my project using a microservices architecture(rabbitmq), one of my worker need to be builded using elixir, when I get message from my queue, for example I want to save it to db, so how do it?

You would call your function like Friends.save(data) from a handler which handles new messages from rabbitmq, just like a phoenix controller which handles new requests.

You wouldn’t need the worker(Task, [&Friends.save/0], restart: :transient) from above.