Unfortunately, getting rid of it is wishful thinking. About the best you can do is manage it such that it won't take over.

One of the problems -- perhaps the major problem -- is that it seeds prolifically. Thus one key is removing it before it seeds.

Then, another part of the problem is that the Soil Seed Bank contains a humongous supply of seeds from years gone by. So, each and every time you disturb the soil, some of those seeds experience the conditions required to sprout and grow.

Another technique is to apply a 2-inch deep mulch when the seedlings are small. (At my place, it's too late for that; they're already in bud and/or bloom.)

As Jean states this does seed prolificaaly, so preventing seed growth is key to control of it. Some sources list this as a summer annual, others as a winter annual, while still others list it asa a winter and summer annual.
A 2 inch mulch is barely adequate to control the growth of much of anything, unless newspaper or cardboard is placed down first, since light can filter through most mulches of that depth and allow plants to grow unimpeded.

I found a heavy wooden mulch like microbark does work without card board, because while one get a few weeds, you get much less then on bare soil. You can pull them as you will only get maybe 3 per day instead of 1000s per day. So, you have to spend hours going over your soil without the mulch, you can do it in just minutes. This is what discourages people too many weeds makes them give up gardening all together. But, this is a non microbarked area. I have a microbarked area, where the lawn used to be.

Around here, the things sprout, grow & flower year-round. (It's the NW climate!) But they are most abundant from fall through late spring.

And yes, 2 inches of mulch *will* stop the seedlings, even here in the NW. Success is in the timing! Apply early in the weeds' life cycle.

Once it sprouts won't it just grow through the mulch?

I was just going to post the same thing. Our lawn, flower and vaggie gardens are filled with this stuff. It gets worse every year. What makes it worse is that one of beighbors doesn't do anything to his lawn (not even mowing or rake leaves) so everything spreads to our yard.

I hand pull everything in the beds but it's impossible to get everything in the lawn. We have used pre-emergents before but with the mild winter, it never went dormant.

I don't like to use chemicals unless it's a last resort but I'm desperate now. Is there any ones that work?