Note that in Russian doctrine as tought in universities, the Cold War never ended.
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You make it sound like NATO was unilaterally pushing for this. Eastern European countries were begging to join NATO. All of them had been independent multiple times over the centuries, always ending up under Russian control. NATO offered a plausible mechanism to end the historical cycle--an historical cycle for which Russia, in 2022, is proudly nostalgic and not afraid to go to war to continue.
Moreover, national security is expensive, especially for small countries who cannot benefit from scale--they need to spend much more for even minimal deterrence. For newly independent nations, NATO provides leverage for their security expenditures. More importantly, it also motivates peaceful resolution of conflict among neighboring NATO states, which makes NATO a keystone institution for peace in Europe, Russia notwithstanding.
And NATO's "peaceful resolution" of European conflict is bunk - ask the Cypriots or the Greeks how NATO tampers Turkish ambitions.
There are plenty of economical and political reasons due to which is it beneficial to keep Latvia and by extension the entirety of Eastern Europe outside of direct or indirect Russian control.
Ukraine is a pretty good example of a country which was mostly ignored both by NATO and the EU so as not to antagonize Russia. It remained a failed state until 2014 and I assume we all know what happened afterwards.