You're correct that you either need to place the camera farther away until the entire field is in view, or use a wide-angle lens adapter (not necessarily "fisheye" but wider). For indoor soccer, clearly you're limited by the walls.
Presumably, you want to hit "record" and enjoy watching the game, rather than having to actively pan the camera back & forth. Also, I'm presuming you only have 1 camera & 1 operator, and you don't really intend to edit the footage together later... If that's the case, look for a wide-angle adapter & put the camera as far away & as high up as possible (a GoPro or similar as suggested previously might be easier to stick high up on the wall :))
For most basic consumer camcorders, you can get a wide-angle adapter to screw onto the front for about ~$40 (make sure the lens & screw threads are the same size or find one specifically compatible for your camera). That should give you ~20-30% wider field of view. It won't be perfect & might be slightly distorted, but it will capture more of the field than you would otherwise.
That still probably won't be enough to capture the entire game from mid-field, but it will get more of it. To fit the whole thing you'd likely need to be up on the ceiling or on a ladder at the top of the bleachers. Not safe, or easy to maneuver.
If you watch professional soccer matches on TV, you'll notice that they don't capture the entire field either, but instead follow the action of the ball. This is because 1) that's the focal point of the game and 2) In order to really see the whole field the camera would have to be so far away you wouldn't really be able to tell what's going on anymore.
There's little/no zooming (instead they cut between cameras). They tend to keep the player w/the ball just off-center, so there's room for them to run & not go out of frame. Mid-range or close-up shots are usually done w/separate cameras, often at field level along the sidelines. As you'd suggested, you could put a camera near the goal line & see the whole field, but then you're down low & will only capture what happens nearby in that half of the field.