Not always. The airline I am about to join emailed me to select an interview date four months after I applied, BA took a couple of weeks, Jet2 about a month, GSS took about 3 months.
An airline is inundated with applications, most of which can been thrown in the bin, but they have to be reviewed by a person(s) nonetheless. This takes time. You never know if whomever is dealing with the CV's or application form is away for whatever reason etc.
If you are sending a CV and cover letter it might be worth having a look at it and see what can make it a little different from your competitors. My professional CV is pretty standard (with a few exceptions) and similar to most 6000hr pilots who worked for Ryanair however it is my personnal side which is different and varied, which I think puts me in the maybe pile at times.
I worked for a brand new airline briefly years and years ago. The amount of postal applications coming through the door each day was ridiculous. I went up there in person and hand delivered it to the main man.
Getting that first job is a nightmare, I have spent a long time on the sidelines. Some people are lucky, some are not.
Good luck.