In MySQL, how can I have non-nullable timestamp column without a default value?
I think that the only way is setting the server variable explicit_defaults_for_timestamp to ON (default is OFF).
This will disable the non-standard behaviour of timestamp columns regarding NULL values:

If explicit_defaults_for_timestamp is enabled, the server disables the nonstandard behaviors and handles TIMESTAMP columns as follows:

It is not possible to assign a TIMESTAMP column a value of NULL to set it to the current timestamp. To assign the current timestamp, set the column to CURRENT_TIMESTAMP or a synonym such as NOW().

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TIMESTAMP columns declared with the NOT NULL attribute do not permit NULL values. For inserts that specify NULL for such a column, the result is either an error for a single-row insert or if strict SQL mode is enabled, or '0000-00-00 00:00:00' is inserted for multiple-row inserts with strict SQL mode disabled. In no case does assigning the column a value of NULL set it to the current timestamp.