One data point is the Urgent Operational Requirement (UOR) [0] experience in the UK military during Operation HERRICK [1], a.k.a. the Afghan campaign. The UK's military acquisition is notoriously glacial but when soldiers started dying because they didn't have the right kit a lot of things were suddenly acquired extremely quickly, for example electronic countermeasures against IEDs, new drones, body armour and a whole range of vehicles that massively reduced crew vulnerability to IEDs. The speed of delivery was partly achieved by cutting the red tape around acquisition, e.g. by not requiring competitive tendering if a 'good enough' already product existed in the market.

This strategy itself created problems for long-term through-life support of a suddenly incoherent vehicle fleet but in turn increased motivation to develop standardised vehicle architectures [2] to allow faster modular upgrades.

This approach isn't going to suddenly deliver a new type fighter aircraft in the timescales of a hot war with China, but it does demonstrate that at least one NATO acquisition system could be speeded up a bit. A current example that is being worked at the moment is how to ramp up supplies of artillery and missiles for supply to Ukraine.

[Edit] Things more generally have slowed down again, e.g. as evidenced by the UK's (failed and cancelled) Warrior Capability Sustainment Programme, a disastrous attempt to upgrade the British Army's primary armoured infantry fighting vehicle.

[0] https://www.gov.uk/guidance/standing-commitments

[1] https://www.gov.uk/guidance/uk-forces-operations-in-afghanis...

[2] https://en.wikipedia.org/wiki/Generic_Vehicle_Architecture

[3] https://en.wikipedia.org/wiki/Warrior_tracked_armoured_vehic...