Cole isn't a noob, but his aggressive play style can be countered.
First, you waited an additional couple seconds before pushing your swordwrath archer up. Yes, I know you were lining up archer first in the event he does the same start, but that costed you early playing time if you did that faster. You queued a miner after your charge. Fair, but I would have done swordwrath in the event of same start and if he goes eco (which he did) queue miner). Either way, you pressured enough for him to get archer. But you're still lacking economically. You make some miners until you see his first spearton. I would have waited. An early unit with his economy size means he's going to push (which indeed he did, successfully I might add). You do not have a castle archer, so your speartons are useless (they would have to retreat, he has nothing force him back). So, how do you get out of this?
You can go the rage method (swordwrath with rage) or boost your economy some before making albows and other units. From there, you can support the purchase of castle archer and leveling the playing field. If he's still knocking at your base, you can knock at his, but it may be wise for a wall investment. Just one is enough to keep the push out until you can albow lock the middle, and eventually ghost.
