Answer in Details
However, it is not strictly mandatory according to Shiva's teachings. Lord Shiva is known as "Ashutosh" (easily pleased) and "Bhola Bhandari" (innocent and generous). He accepts sincere devotion regardless of strict rituals or timings. What matters most is the purity of heart, devotion, and faith.
If circumstances make it difficult to perform puja before breakfast (due to health, schedule, or other constraints), you can perform it at another suitable time. The intention and devotion with which you worship are more important than the specific time.
In summary, while it is traditional and considered auspicious to do Shiv Puja before breakfast, it is not mandatory. Sincere devotion at any time is always accepted by Lord Shiva.