Yes, you can give up Google Search and ultimately other Google services too!
Here are some tips and advice on eliminating Google from your life.

Search Engine:
A start is to use another search engine like
https://duckduckgo.com
or if you are using Tor browser.
https://3g2upl4pq6kufc4m.onion/

Syncing and Google Drive replacements:
Giving up Google Drive may seem tedious because Google’s famous cotton candy appeal however if you value Privacy, Security and 100% control over your data, there are alternatives.

A Google Drive “File Sharing” alternative – Onion Share

OnionShare is an open source tool that lets you securely and anonymously share a file of any size.

Disclaimer, Like all software, OnionShare may contain bugs or vulnerabilities and you should consult an expert if you have concerns

OnionShare lets you securely and anonymously share files of any size.

It works by starting a web server, making it accessible as a Tor Onion Service, and generating an unguessable URL to access and download the files.

It does not require setting up a separate server or using a third party file-sharing service.

You host the files on your own computer and use a Tor Onion Service to make it temporarily accessible over the internet.

The receiving user just needs to open the URL in Tor Browser to download the file.

Links:
https://onionshare.org/
or http://lldan5gahapx5k7iafb3s4ikijc4ni7gx5iywdflkba5y2ezyg6sjgyd.onion/ (Requires Tor Browser 7.5+)

A great tool for keeping files in sync is Syncthing (https://syncthing.net)

• Syncthing is a Free/Libre program that has a small learning curve but is very useful for keeping folders in sync across multiple computers.
• Syncthing is Private. None of your data is ever stored anywhere else other than on your computers. There is no central server that might be compromised, legally or illegally.
• Syncthing is Encrypted. All communication is secured using TLS. The encryption used includes perfect forward secrecy to prevent any eavesdropper from ever gaining access to your data.
• Syncthing is Authenticated. Every node is identified by a strong cryptographic certificate. Only nodes you have explicitly allowed can connect to your cluster.

Syncthing does take a little time getting use to however is well worth learning.

Here are some guides that I found useful when I made the decision to use it.
• Setting up Syncthing:

Another alternative to Google Drive is Nextcloud
Disclaimer, I have personally never used NextCloud up to the time of this posting.

For the purpose of this guide I will point out the most relevant things you can get out nextcloud which include self-hosting, DAV, Cloud platform and sync tools.

I aim to write a Nextcloud tutorial in the future, so please follow me if you would like to join in the fun and learn how to do it yourself when I publish it.
BONUS TIP: Start Using Tor Browser – https://www.torproject.org