Usually, things can take very long with Google lately. This is because there are many changes, especially in the EU. In some niches and for certain keywords things move a little faster. Then you can expect to be on the first page within a month or so. Keep in mind that you don't overoptimize your site and don't use too many exact keywords when you are linking to your site. It really always depends.
It takes 3-6 months for a decent site to be ranked number one. You shouldn't stress on this topic because that is what Google wants the SEOs to hurry and do mistakes.
Don't listen to the people that tell you that you can rank quickly because they are often times not ranking it is just warm air.
You can look at some rankings with tools like
SERPed or
AHREFs to find out the average time that it takes to do a proper
Search Engine Optimization.
Remember that it is better to under optimise than overdoing stuff. You can always be more aggressive with your link building (PBNs, Blog Posting, Forum Posting,...)
As soon as you Google things that you are trying to force them to place your page number one there is a high chance of getting a penalty.
PS: Rome wasn't built in one month, it took several months and years for the world to know who was the new #1.