1. Offer Food and Water: Start by placing some food and water near the stray cat's hiding spot. This will help build a positive association and encourage the cat to approach you. Gradually move the food closer to your location over time, allowing the cat to get used to your presence.
2. Use Gentle Body Language: When approaching a stray cat, it's important to use calm and non-threatening body language. Avoid direct eye contact, as it can be seen as aggressive. Instead, blink slowly to show that you mean no harm. Sit or crouch down to appear less intimidating and extend your hand slowly for the cat to sniff and approach at its own pace.
3. Establish Trust through Play: Play is a great way to bond with a stray cat and build trust. Use interactive toys, such as feather wands or laser pointers, to engage the cat in play. This will help redirect their energy and create positive experiences with you. Remember to be patient and allow the cat to initiate and set the pace of play.
4. Provide Shelter and Comfort: Creating a safe and comfortable space for the stray cat can aid in gaining their trust. Place a cozy bed or blanket in a quiet area where they feel secure. Offering a shelter, such as a cat house or a designated outdoor feeding station, can also provide a sense of security and encourage the cat to stick around.
5. Consult with Local Animal Organizations: If you encounter difficulties or have concerns about a stray cat, it's always beneficial to seek guidance from local animal organizations. They can provide advice, resources, and even assist in trapping and neutering the cat to help control the stray population.

Remember, gaining the trust of a stray cat takes time and patience. It's important to respect their boundaries and let them approach you on their terms. With consistent effort and positive experiences, you can build a strong bond and provide a safe and loving environment for the stray cat to thrive.

If you need further assistance or have any more questions, feel free to ask!