The solution I use most - there are several - is to position the needle at least an 1/8th of an inch from the edge of the fabrics your are piecing.
You can also use what is called a 'leader' - just a small scrap of two fabrics that you put under the needle - and start your sewing on that. When you reach the end of the leader, do not lift the foot, just place the triangle you are piecing near it and start sewing. It's really just an adaptation of the chain piecing technique.
Others will chime in with even more solutions. Quilters are a resourceful bunch of people.