Yes, bras can be sewn. I wanted to try making some, and I stumbled across a cute pattern on Etsy.
The pattern is called Brigette Triangle Bra by OhhhLuluSews. It was a PDF pattern, so the download was quick and easy.
There are so many styles of bras out there, and I wanted something simple and comfortable. I made one, and it is pretty good.
I don't like frills and girly embellishments, so I just went with simple contrast of blue and white.