The appraisal is part of a Buyer's investigative contingency rights and is not part of the escrow, per se; but rather, more connected to the Residential Purchase agreement.
The deadlines of your transaction, and the duties of both Buyer/Seller, are clearly spelled out in the Residential Purchase contract you signed. You have every right to obtain a copy of the contract you signed and explore these timelines and duties yourself, if desired. In addition, you can refer to the following chart that outlines the "typical" cadence of a transaction from the viewpoint of both Buyer/Seller; however, understand that the default dates shown may be different than what was ultimately agreed to.:
Appraisal - the property must appraise at the value agreed to, or greater. If less, the buyer must bring more money to the escrow table to close the deal, the Seller must lower the price of the home, or the buyer may cancel the contract within the Appraisal contingency period.
However generally the appraisal report takes 7-14 days depending on thier back log.
Let your agent know you want a copy of the appraisal.
Escrow is almost always opened within 24 hours of the accepted offer,signed by both the seller and the buyer.
Good luck and congratulations on your purchase.