A short word that is used when one finds something unexpectedly

I suspect you may be looking for 'lit' or 'lighted'

Per the OED

to light on or upon (or of): to happen to come upon, chance upon; to meet with or discover, esp. unexpectedly or by accident; to come across, whether as the result of search or not.

They give the following examples:

1738 J. Wesley Wks. (1830) I. 38 I called at Alringham, and there lit upon a Quaker.

1867 E. A. Freeman Hist. Norman Conquest (1876) I. 547 I have as yet only once lighted on the use of the word in the singular.

Some more recent citations from around the web:

Going over this old ground, she poked through the pile of papers she had brought with her to chaperone her during her dinner. There was the card for the children there were the lecture notes, there was the note she had written to Karel. She tore it up, and pushed the pieces into the folder. The folder was full of such scraps. Then, wavering, she lit upon another new postcard -

The Realms of Gold: A Novel Margaret Drabble 2013.

And when I lit upon the moral philosophy of Immanuel Kant, I knew I had found what I was searching for.

Mark D White Kantian Ethics and Economics Autonomy, Dignity and Character copyright 2018 Stanford University Press

Did you mean stumble?

4 a : to come unexpectedly or by chance

_{(source: Merriam-Webster)}

I was looking through that old chest of draws upstairs when I stumbled upon a rather suspicious looking package.

looks pretty natural to me.

You could use happen upon:

: to find or meet (someone or something) by chance

// She happened on a little cottage in the woods.

// I happened upon them at the grocery store.

Not the single word you're looking for, but this phrasal verb fits perfectly.

"I was browsing through Stack Exchange the other day when I came across a most challenging question."

come across - "if you come across something or someone, you find them or meet them by chance."

Example sentences:

I came across a $100 bill on my way to work yesterday!

I came across Peter at the bookshop after work.

If you come across my wallet, please let me know. I forget where I left it.

According to Merriam-Webster Dictionary:

bump into
to encounter especially by chance.

Though it is quite informal, but short and metaphorical.