It may be better to use REAL type, to save storage space.
Quote from 1.2 section of Datatypes In SQLite Version 3
SQLite does not have a storage class set aside for storing dates and/or times. Instead, the built-in Date And Time Functions of SQLite are capable of storing dates and times as TEXT, REAL, or INTEGER values
CREATE TABLE test (
id INTEGER PRIMARY KEY AUTOINCREMENT,
t REAL DEFAULT (datetime('now', 'localtime'))
);
see column-constraint .
And insert a row without providing any value.
INSERT INTO "test" DEFAULT VALUES;