Can I apply for my spouse and children's DTV dependent visas before entering Thailand after my DTV application approval?

As soon as your visa is approved it is active so you do not need to enter Thailand first.

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PRINT OUT THE EMAIL THAT HAS YOUR DTV VISA.

That's what you should do... print it out.

You may have to show PROOF of your DTV Visa to airline staff on check-in for your flight ✈️ to Thailand...even to the connecting airline staff. Or to the land border crossing entry Thai Immigration Officer.

Upon arrival into Thailand, show the DTV visa to the Thai Immigration Officer and look at the STAMP placed in your passport to be sure you are STAMPED in for 180 days.

You don’t have to enter Thailand before. Just apply for dependents after yours is approved

As soon as yours is approved yes. And no yours are not affected