My house is going on the market June 1 but I found a house I love now. How do I approach this with my realtor?

Title says it all. My house is going on the market June 1, and I finally found a home that checks all my boxes. Perfect location, older character home with upgrades, etc. Price is also right in my sweet spot, but I could potentially bid higher if it came to that. I’ve been casually looking for awhile so I know how rare this particular home is and I’m chomping at the bit to see it and potentially make an offer. I expressed this to my realtor and he said it’s too early since my home won’t go on the market until the 1st. I completely understand, so I asked him to please put a bug in the listing agent’s ear to let them know I’m a potential buyer. Is there anything else I can do to make sure I have a chance before it goes contingent and my house is listed? Again, I could potentially offer more than listing if that helps. TIA!