Antidepressants typically begin working within 3-12 weeks. There is no way of speeding this up, new neurons take time to bud, grow and mature.
However, you could try taking hydroxyzine (Vistaril) to ease anxiety until the escitalopram kicks-in. Hydroxyzine is a prescription antihistamine with anti anxiety properties. It isn't as potent as the benzodiazepines (BZDs), but is often potent enough to make a significant difference and unlike the BZDs it doesn't block neurogenesis.
*Hydroxyzine comes in two forms, hydroxyzine pamoate (Vistaril) and hydroxyzine hydrochloride (Atarax). Anecdotally, the pamoate form is supposedly the more effective anxiolytic.