When is the best time to apply for an ITIN?
It is possible to apply for an ITIN number at any time during the year. However, if you file a 1040 NR tax return along with the ITIN application (most cases), then you can incur late fees and interest charges when filing past the tax deadline of April 15.
The late fees and interest charges accrue according to Topic no. 653. You can use this IRS penalty calculator to forecast potential penalties you could incur. In general, the fees and interest will reach a maximum of 100% of the tax owed. So if you owe $10 USD in taxes, the most you can possibly owe is $20 USD.