Remove the floor trim from around the perimeter of the room using your pry bar and hammer. Keep it intact as you remove it. Set it aside.
Roll out a course of plastic foam underlayment on top off the tile, on the edge of the room where you want to start. Use your razor knife to cut the strip to size
Lock two engineered wood floating floorboards to each other at their ends, snapping them as instructed -- systems vary. Set them at one end of the floor, on the underlayment. Put spacers between the wall and the board to keep them slightly out from the wall.
Set additional boards along the wall end to end, putting spacers alongside all of them. Use a miter saw to cut the last board as needed.
Lay the second course alongside the first, locking the boards in place by the fittings on their long sides. Set the boards in varied sizes so the ends are staggered between courses.
Build across the floor course by course, laying out additional underlayment as necessary. Continue staggering the boards from course to course and cutting the final board of each course as necessary.
Cut the last final course along their lengths on a table saw so they fit along the ending wall, leaving a 3/8 inch space at the wall.
Re-install the trim with your hammer and trim nails. The trim will hide the gaps around the edges of the floor.