I'm a little puzzled. The minimum you can get from 10 levels (after level 30) is 8200 BE, which is more than enough for one champion, and easily enough for two or three lesser-priced champions. That's not even counting the 40% discount you get on using BE to upgrade a champion, which makes that enough for two 6300 champions with some left over.
Add to that the free Ashe at level 2, the free Garen at level 3, the free Brand at level 3, Tristana/Alistar (who you can get for free), Xin Zhao shard at 6, the assured Caitlyn/1350/3150/4800 shard at level 5, the assured 450 shard at 10, the assured 1350 shard at 11, the two assured 1350 shards at 18, the 4800 shard at 20, the 3150 shard at 22, 27, and 29, and the 450 shards at 27 and 29, and you've received 15 champions/shards ignoring every other champion capsule. You've also received (counting the champion capsules NOT mentioned as assured) 13,535 in BE value from the other capsules offered, which is enough to outright buy the bulk of the non-6300 champions you've gotten in those shards.
If you're buying expensive champions, sure -- you won't have enough. But you can DEFINITELY get a functional ranked pool pretty quickly.