CS3 on Mac OS Big Sur [CS3 is dead]

Even if you could activate legacy Creative Suite 2, 3 or 4 (which you can't), they won't run much less install on modern macOS.  Creative Suite is 32-bit software and thus incompatible with radically new 64-bit architecture.

See links below about Big Sur & M1 Chip compatibility

https://helpx.adobe.com/download-install/kb/macos-big-sur.html

https://helpx.adobe.com/download-install/kb/apple-silicon-m1-chip.html

MODERN OPTIONS:
Photoshop Elements (approx $100, no subscription needed).
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan (approx $10/month for 12 months). Includes the following:
- Photoshop CC and Photoshop on iPad
- Lightroom on desktop, mobile and the web
- Lightroom Classic
- Portfolio website + hosting
- Spark with premium features
- Bridge
- 20 GB cloud storage (upgradable to 1 TB).
https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (51 + apps & services) and Single Apps Plans
https://www.adobe.com/creativecloud/plans.html

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Beware of fake Adobe reps who may contact you privately offering to sell you software or take control of your computer. It's a scam, run away!
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3 Easy Ways to Identify Genuine Adobe Staff
https://tinyurl.com/10791730

You can't install CS3 anymore. The activation servers have been shut down.