SHORT ANSWER
Among the many thousands who joined the gold rush and dug with their own hands, a few struck it rich but couldn't be called 'exceedingly wealthy'. Many more gathered a decent sum before (wisely) packing it in and setting off back home. The large majority, of course, found little or else squandered their gains.
One non-supplier who did become very wealthy was John C. Frémont, later to become the first Republican candidate for President, but he got rich when substantial gold deposits were discovered on his property; as far as I can tell, he did not mine himself.
The other (more valid cases in terms of miners or prospectors) listed below did not become especially wealthy as result of digging with their own hands but are worth mentioning for one reason or another.
DETAILS
John Sullivan
John Sullivan, who dug up $26,000 in the summer of 1848, was one of the few who both struck it rich and made good use of his new-found wealth.
Sullivan was one of the fortunate few to find a true “gold nugget” in
what became known as Sullivan’s Creek. The profits from this find were
used to purchase and develop many of San Francisco’s noteworthy
properties, including the Palace Hotel, Holy Cross and Old St. Mary’s
churches. He also was the founder and first President of Hibernia
Savings and Loan Society.
'Chino' Tirador
Mr. Tirador may well hold the record for squandering the largest amount of gold in the shortest time. Chino
...dug four feet down to bedrock and then spent the next seven hours
picking up nuggets enough to fill a wooden batea (a Mexican gold
panning bowl) so full that he could scarcely lift it.
If indeed he could 'scarcely lift it', this may have meant more 100 pounds. So far, so good, but by 10pm that same night it was all gone:
He paid two pounds of gold dust for a bottle half full of aguardiente
and then shopped around the camp for silver coins ...so he could
gamble. He obtained these by paying one ounce of gold for $2.50 in
coin. By ten o'clock that night he was dead drunk and flat broke.
Seven white miners and 50 Indians
This group found 273 pounds of gold in 2 months by the Feather River. The Indians got only 13 pounds, leaving an average of over 37 pounds for each of the white miners.
William Gulnac
Of Mexcian origin, Gulnac was granted the Rancho Campo de los Franceses in 1844 but sold it to his former partner Charles Weber (founder of Stockton) in 1845 after failing to settle the ranch.
It seems he then turned to prospecting for, in around 1848, he dug up the second largest nugget found in California at Wood's Creek in Tuolumne County. Weighing 150 pounds, the nugget contained 75 pounds of gold. Gulnac did not live long to enjoy the proceeds of his find for he died in 1851.
Alvin Aaron Coffey
Not large amounts here, but enough for a slave to buy his and his family's freedom (so wealth in another sense). Alvin Coffey found $5,000 in gold in 1850 and another $7,000 in 1854.
The first amount was simply taken by his owner, a Dr. Bassett, who then sold him to one Mary Tindall. Her husband, Nelson, already owned Coffey's wife and children:
He agreed to let Coffey buy his way to freedom. In 1854, Coffey
returned to California and earned $7,000 in the goldfields, enough to
free himself and his family.
Coffey, who died in 1902, wrote an autobiography.