There is insufficient evidence in the provided sources to verify Kristi Noem's claim that Los Angeles would not be standing today if President Trump had not taken action.
Kristi Noem: "I do know that LA wouldn't be standing today if President Trump hadn't taken action."

Trump picks Kristi Noem for Homeland Security secretary. Here’s what to know - PBS News
Source: pbs.org
Key Evidence
None of the seven provided sources mention any threat to Los Angeles that was averted by President Trump’s actions ( through ).
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The sources focus on Kristi Noem’s political roles and controversies but do not support the specific claim about LA’s survival.
theguardian.comtheguardian.comKristi Noem: the made-for-TV official executing Trump’s mass deportations
pbs.orgpbs.orgTrump picks Kristi Noem for Homeland Security secretary. Here’s what to know+1 more
No official statements or credible news reports confirm that LA’s existence depended on Trump’s intervention.
What the Evidence Shows
The claim by Kristi Noem that "LA wouldn't be standing today if President Trump hadn't taken action" is a definitive statement attributing the survival or continued existence of Los Angeles to actions taken by former President Trump.
None of the provided sources directly address or corroborate this specific claim about Los Angeles. The sources primarily focus on Kristi Noem's role as Secretary of Homeland Security under Trump, her nomination and confirmation, and some controversies related to her statements and actions.
The sources do not mention any event or circumstance where Los Angeles was at risk of ceasing to exist or being destroyed, nor do they link such a scenario to Trump's interventions.
Without direct evidence or official documentation supporting the claim, it remains an unverified assertion.
Given the lack of corroboration from multiple independent, reliable sources, this statement should be treated as an unverified political claim rather than a factual statement.
It is also important to note that such a sweeping claim about a major city like Los Angeles would likely be widely reported and documented if true, yet no such evidence appears in the search results.
In conclusion, based on the available evidence from the provided sources, this claim cannot be substantiated and should be considered unverifiable.