You don't need arcane bolt
period! There are handful of ways to start the game optimally.
There is 1 skill and 1 stat book that you got free from bioware as a downloadable. It came from completing the 2D flash game I think.
Mage should always put every point into magic at the start. This means that you should have an opening Magic stat of 21 + 3 from the stat book. You gain your very first level up just after you speak with the sloth bear in the fade.
This means you should be on 27 Magic and be able to collect the fireball spell. The 2nd levelup occurs just after you fight the spiders.
with the no starting talents modChoose Flame burst, Flame Weapons, Winters grasp and then pick Fireball at level 2
without the no starting talents modArcane bolt is chosen for you
Choose Flame burst, Winters grasp, Then Flame Weapons at level 2, Fireball at level 3
Flame burst + winters grasp is enough to kill everything untill you fight the headless ghosts in the dungeon.
It is possible to go for other spells such as shock or cone of cold, however fireball is the most usefull in the early game because it is a ranged AOE spell that does very good damage and has a 4 second burn. It is particularly usefull vs pesky archers who are your only real threat as a mage.
The "Mage" line of spells has no real use. I would agree with the OP and say Don't bother

Arcane bolt is a straight damage spell with no standout special effects. It gets resisted alot and it has a slow flight speed. Offensive mages need to maximize the amount of units they damage with any given cast and there are far better ways to do this than by spaming arcane bolt.
Arcane shield is a spell that mages never need. It only bumps your defense up to the level of a warrior. "Glyph of repulsion" is a far more usefull spell and is vastly superior in damage mitigation.
Staff focus increases your staff weapon damage by 1/3rd however if your in a position where you are routinely using a staff you are doing something very wrong.
Arcane Mastery gives a spellpower bonus of 5. A 4th tier talent that only increase spellpower by 5???