There's nothing suspicious in building backlinks right away, a new website can and should start reaching out to seek advertising as soon as they start their online appearance, Google aren't stupid, they know that web development and digital marketing often offered together.
That being said, I also recommend doing stuff "slowly and steady", in many (real) cases, businesses wouldn't like to spend their entire marketing budget in online if they just started building a website and didn't see income from it yet.