Storing Backups on Google Cloud (free/lowcost how ?)
To backup you data at Google Cloud you can use Google Cloud Storage instead of copying backup data to AWS bucket.
Have a look at the documentation Storage classes to find more details:
Nearline Storage is a low-cost, highly durable storage service for storing infrequently accessed data. Nearline Storage is a better choice than Standard Storage in scenarios where slightly lower availability, a 30-day minimum storage duration, and costs for data access are acceptable trade-offs for lowered at-rest storage costs.
and
Coldline Storage is a very-low-cost, highly durable storage service for storing infrequently accessed data. Coldline Storage is a better choice than Standard Storage or Nearline Storage in scenarios where slightly lower availability, a 90-day minimum storage duration, and higher costs for data access are acceptable trade-offs for lowered at-rest storage costs.
and
Archive Storage is the lowest-cost, highly durable storage service for data archiving, online backup, and disaster recovery. Unlike the "coldest" storage services offered by other Cloud providers, your data is available within milliseconds, not hours or days.
Unlike other Cloud Storage storage classes, Archive Storage has no availability SLA, though the typical availability is comparable to Nearline Storage and Coldline Storage. Archive Storage also has higher costs for data access and operations, as well as a 365-day minimum storage duration. Archive Storage is the best choice for data that you plan to access less than once a year.
After that, have a look at the documentation Object Lifecycle Management:
To support common use cases like setting a Time to Live (TTL) for objects, retaining noncurrent versions of objects, or "downgrading" storage classes of objects to help manage costs, Cloud Storage offers the Object Lifecycle Management feature.
and at the section SetStorageClass cost advantages:
Unlike changing an object's storage class manually, Object Lifecycle Management does not rewrite an object when it changes the object's storage class. This gives Object Lifecycle Management certain pricing advantages:
There are no retrieval fees or early deletion fees associated with the storage class change, even when the object is originally set to Nearline Storage or Coldline Storage.
The object's time spent set at the original storage class counts towards any minimum storage duration that applies for the new storage class.
To estimate cost of usage you can use GCP Pricing Calculator.