MySQL - Fetch millions of data in chunk with constantly changing data

Question

Below is the schema of my table A.

CREATE TABLE A (
      NAME VARCHAR(255),
      CREATED_AT DATETIME DEFAULT CURRENT_TIMESTAMP,
      UPDATED_AT DATETIME DEFAULT CURRENT_TIMESTAMP,
      PRIMARY KEY(NAME)
);
CREATE INDEX I1 ON A (UPDATED_AT,CREATED_AT);

Now we have around 50M records in this table. I can't fetch all the data at once as it would cause memory issues in the backend. I was thinking to use OFFSET+LIMIT combination to fetch the data in chunks but the problem is that the data is updating after every 5 minutes which can alter the position of the record in the table as we have the index on UPDATED_AT.

We can't afford to read the record twice. Is there any other way to read a large amount of data in chunks with frequent data updates.