At this time in the northern emisphere you can grow seedlings outside
as well as inside. Inside is for starting seeds in the cold season.
Inside you will have problems with damping off (seedlings die, the stem
having wilted), with not enough light, and with the seedlings not
having UV protection (they need to feel the UV to start producing it).
These problems generally are absent outside. The cover tends to promote
damping off so I use the covers as trays and never cover my seeds.

If it is only the birds bothering you, cover the trays with chicken
wire. Some seeds, incidentally, need light to germinate. Most other
seeds are indifferent. No seed needs absolute darkness. All seeds need
a minimum temperature and moisture. I do sprout my seeds inside in near
darkness but only because I use the top of my fridge, which is warm, to
sprout them quickly. In the summer, the same seeds are sprouted outside
in full sunlight.