The phrase "I first suggested" is correct and usable in written English.
However, it can depend on the context in which you use it. For example, "I first suggested that we try a different approach but no one wanted to listen."
– I'm not as reliable as I first suggested.
When I first suggested Spanish A-level to my editor for this piece, she replied, "Great!
I first suggested R. Chasuble, after Reverend Chasuble, the priest in Oscar Wilde's "The Importance of Being Earnest".
"When I first suggested to my kids that they do a cross-country run, they said it sounded like torture or punishment," he says.
When I first suggested reaching out to our competitors, Kevin, my co-founder, was skeptical but hopeful that the other companies would respond.
"Two years ago, when I first suggested they meet each other, they approached the blind date with disdain and a lot of sarcasm".
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The most frequent question I'm asked is what happened at that initial lunch meeting with Ernestine Fu where she first suggested I work with Alsop Louie Partners.
In my early twenties, when doctors first suggested I get tested for the BRCA1 and BRCA2 mutations, they explained that if I tested negative, I wouldn't have to begin regular mammograms until the age of 35.
I'd love to discuss this more with you but I'd first suggest that you perhaps consider ratcheting your potion down to the 30-50 minute range instead of 3-5 hours.
I offered to pay by credit card or check, but the bridge didn't accept either, and the toll taker at first suggested I could go back to an ATM in town, but they would charge me $25.
