What's the meaning of this phrase in this sentence? "The plan is to hit the ground running for the next year." Also, can I use the phrase with "to"? like this↓? "I am going to hit the ground running to start the plan" Sorry for gramatically incorrect sentences cuz I'm not a native.
The phrase is a metaphor. It is becoming what was designated many years ago by Fowler as a dead metaphor in that it refers to an image that is no longer clear or even relevant.
The idea behind the image is that if you are on some military mission involving jumping out of a vehicle and immediately springing into action, then you are "hitting the ground running" as distinct from gathering yourself together, making sure you have all your kit with you, have consulted your map, have spoken to your superior officer et cetera et cetera.
Unless you are certain that your superiors like that kind of language, you would be advised to say something like "I am ready and will start putting the plan into action immediately".
The dictionary meaning on google is "start something and proceed at a fast pace with enthusiasm."
In your example "The plan is to hit the ground running for the next year" I'm sure the speaker means to say that they plan to be ready to start and make quick/significant progress next year. However, the use of "for" makes it unclear if they intent to start today and make progress that will set them up for next year.
Your second example, "I am going to hit the ground running to start the plan" is redundant - "Hitting the ground running" already involves the idea that you're starting something. It would be more colloquially correct to say "For this plan, we want to hit the ground running"