The best time to look for a job is when you already have one. You have income, you're not desperate, and you can afford to be selective. But you need to be careful.
Keep It Confidential
Don't tell colleagues you're looking. Don't use your work email or computer. Be especially careful about LinkedIn — turning on "Open to Work" publicly will be visible to anyone, including your current employer.
Use LinkedIn's Private Mode
LinkedIn lets you signal to recruiters that you're open to opportunities without broadcasting it. Go to Settings → Job seeking preferences → "Share with recruiters only."
Schedule Interviews Strategically
Request early morning, lunchtime, or end-of-day slots. Use personal days or vacation time for multi-round interviews. Many companies do first rounds by video call, which is easier to manage.
Keep Performing at Your Current Job
Don't let your work quality slip. You still need that reference, and your job search might take longer than expected. Leave on your own terms, not because performance issues forced the issue.