We fill the HSA first, then trad 401k before IRAs. For us, HSA and traditional 401k decrease our AGI AND line 7 wage income, which increases our refundable credits (EITC, also matched by our state at 30%). Trad IRA contributions can't reduce line 7 wage income, so won't increase EITC.
Of course, at that point we hit zero fed tax, so there's no point to additional traditional contributions. The tax refunds then go to maxing Roth IRAs for each of us.
If you are income eligible, could you contribute to BOTH an IRA and 401k?