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This bank at the corner of Sealy & Hardie in 1907 is probably the

Alvin State Bank.

That is significant because The First National Bank of Alvin, charter 7070, was only in business
for 2 years and 1 month, from December 21, 1903 to January 31, 1906.

When The First National Bank of Alvin closed on January 31, 1906, the Alvin State Bank opened its doors the next morning on February 1, 1906.

It cannot be coincidence that The First National Bank of Alvin liquidated, and the Alvin State Bank opened within 24 hours. The Alvin State Bank has to be the successor to The First National Bank of Alvin. And what we are looking at in the photo above is The First National Bank of Alvin building in 1907.

This is the intersection of Sealy and Hardie today.

There was a First National Bank in Alvin, charter 12580, seemingly not connected to the of Alvin bank, and not an issuer of currency. It ceased business on April 22, 1931.

The First National Bank of Alvin only printed 1902 Red Seals. The total issue was $9,300 with $550 not redeemed.
There are no notes reported in the census.