Our home yard is all rock (desert) so that is what my puppy is used to, but our trainer's yard has the most beautiful fluffy green grass ever! I started talking my puppy there at 3 months and he couldn't focus for the life of him! He was doing the same things you described. At the suggestion of my trainer, I got there 10 minutes early and let him explore a bit before the real training began. That helped a bit, but what has helped the most is his aging...so time will be on your side. He is now 5.5 months and every week gets better, but my trainer is great and says let him be a pup.
Beyond that...when you are outside, get the dog excited! Take off running and call his name and make some noise, squeak some toys (make a fool of yourself in other words) and puppy will definitely be interested in YOU! Then get one 30 second training and off you go again! Make it fun, fun, fun! Be better than the grass and twigs. It's all about engagement right now and making the dog love to be with you...then he will work for you!
I learned this from recent experience...except I had to act like a fool in front of the other dogs and their handlers! Lol