No, you must buy AppleCare+ within 60 days of the purchase. And your limited warranty did not cover loss or theft, only AppleCare+ with Loss and Theft would have covered it.
You can see if your homeowners insurance covers it, and, if you purchased it with some credit cards their loss coverage may help.
In general, you can’t buy any insurance after the fact. Think about it: I could purchase life insurance on someone after they died, or on my house after it burned down.
George Bernard Shaw wrote an essay explaining insurance: On the Vice of Gambling and the Virtue of Insurance. I couldn’t find any reprints of it to link to, but it is hilarious and covers your question very well.